diff --git a/lib/matplotlib/__init__.py b/lib/matplotlib/__init__.py
index 9731a683bcb7..3b3c5191d80a 100644
--- a/lib/matplotlib/__init__.py
+++ b/lib/matplotlib/__init__.py
@@ -176,16 +176,14 @@ def _get_version():
         return _version.version
 
 
-@functools.lru_cache(None)
-def __getattr__(name):
-    if name == "__version__":
-        return _get_version()
-    elif name == "__version_info__":
-        return _parse_to_version_info(__getattr__("__version__"))
-    elif name == "URL_REGEX":  # module-level deprecation.
-        _api.warn_deprecated("3.5", name=name)
-        return re.compile(r'^http://|^https://|^ftp://|^file:')
-    raise AttributeError(f"module {__name__!r} has no attribute {name!r}")
+@_api.caching_module_getattr
+class __getattr__:
+    __version__ = property(lambda self: _get_version())
+    __version_info__ = property(
+        lambda self: _parse_to_version_info(self.__version__))
+    # module-level deprecations
+    URL_REGEX = _api.deprecated("3.5", obj_type="")(property(
+        lambda self: re.compile(r'^http://|^https://|^ftp://|^file:')))
 
 
 def _check_versions():
diff --git a/lib/matplotlib/_api/__init__.py b/lib/matplotlib/_api/__init__.py
index 2e473c474526..43b25908832e 100644
--- a/lib/matplotlib/_api/__init__.py
+++ b/lib/matplotlib/_api/__init__.py
@@ -10,6 +10,7 @@
 
 """
 
+import functools
 import itertools
 import re
 import sys
@@ -189,6 +190,41 @@ def check_getitem(_mapping, **kwargs):
             .format(v, k, ', '.join(map(repr, mapping)))) from None
 
 
+def caching_module_getattr(cls):
+    """
+    Helper decorator for implementing module-level ``__getattr__`` as a class.
+
+    This decorator must be used at the module toplevel as follows::
+
+        @caching_module_getattr
+        class __getattr__:  # The class *must* be named ``__getattr__``.
+            @property  # Only properties are taken into account.
+            def name(self): ...
+
+    The ``__getattr__`` class will be replaced by a ``__getattr__``
+    function such that trying to access ``name`` on the module will
+    resolve the corresponding property (which may be decorated e.g. with
+    ``_api.deprecated`` for deprecating module globals).  The properties are
+    all implicitly cached.  Moreover, a suitable AttributeError is generated
+    and raised if no property with the given name exists.
+    """
+
+    assert cls.__name__ == "__getattr__"
+    # Don't accidentally export cls dunders.
+    props = {name: prop for name, prop in vars(cls).items()
+             if isinstance(prop, property)}
+    instance = cls()
+
+    @functools.lru_cache(None)
+    def __getattr__(name):
+        if name in props:
+            return props[name].__get__(instance)
+        raise AttributeError(
+            f"module {cls.__module__!r} has no attribute {name!r}")
+
+    return __getattr__
+
+
 def select_matching_signature(funcs, *args, **kwargs):
     """
     Select and call the function that accepts ``*args, **kwargs``.
diff --git a/lib/matplotlib/_api/deprecation.py b/lib/matplotlib/_api/deprecation.py
index 1323103ff541..363bb5f7a023 100644
--- a/lib/matplotlib/_api/deprecation.py
+++ b/lib/matplotlib/_api/deprecation.py
@@ -150,13 +150,14 @@ def finalize(wrapper, new_doc):
                 return obj
 
         elif isinstance(obj, (property, classproperty)):
-            obj_type = "attribute"
+            if obj_type is None:
+                obj_type = "attribute"
             func = None
             name = name or obj.fget.__name__
             old_doc = obj.__doc__
 
             class _deprecated_property(type(obj)):
-                def __get__(self, instance, owner):
+                def __get__(self, instance, owner=None):
                     if instance is not None or owner is not None \
                             and isinstance(self, classproperty):
                         emit_warning()
diff --git a/lib/matplotlib/backends/backend_gtk3.py b/lib/matplotlib/backends/backend_gtk3.py
index bf134f33963c..46b48c2200aa 100644
--- a/lib/matplotlib/backends/backend_gtk3.py
+++ b/lib/matplotlib/backends/backend_gtk3.py
@@ -37,11 +37,11 @@
     Gtk.get_major_version(), Gtk.get_minor_version(), Gtk.get_micro_version())
 
 
-# module-level deprecations.
-@functools.lru_cache(None)
-def __getattr__(name):
-    if name == "cursord":
-        _api.warn_deprecated("3.5", name=name)
+@_api.caching_module_getattr  # module-level deprecations
+class __getattr__:
+    @_api.deprecated("3.5", obj_type="")
+    @property
+    def cursord(self):
         try:
             new_cursor = functools.partial(
                 Gdk.Cursor.new_from_name, Gdk.Display.get_default())
@@ -54,8 +54,6 @@ def __getattr__(name):
             }
         except TypeError as exc:
             return {}
-    else:
-        raise AttributeError(f"module {__name__!r} has no attribute {name!r}")
 
 
 # Placeholder
diff --git a/lib/matplotlib/backends/backend_wx.py b/lib/matplotlib/backends/backend_wx.py
index 4ba85f505151..16b152a51689 100644
--- a/lib/matplotlib/backends/backend_wx.py
+++ b/lib/matplotlib/backends/backend_wx.py
@@ -41,25 +41,19 @@
 PIXELS_PER_INCH = 75
 
 
-# module-level deprecations.
-@functools.lru_cache(None)
-def __getattr__(name):
-    if name == "IDLE_DELAY":
-        _api.warn_deprecated("3.1", name=name)
-        return 5
-    elif name == "cursord":
-        _api.warn_deprecated("3.5", name=name)
-        return {  # deprecated in Matplotlib 3.5.
-            cursors.MOVE: wx.CURSOR_HAND,
-            cursors.HAND: wx.CURSOR_HAND,
-            cursors.POINTER: wx.CURSOR_ARROW,
-            cursors.SELECT_REGION: wx.CURSOR_CROSS,
-            cursors.WAIT: wx.CURSOR_WAIT,
-            cursors.RESIZE_HORIZONTAL: wx.CURSOR_SIZEWE,
-            cursors.RESIZE_VERTICAL: wx.CURSOR_SIZENS,
-        }
-    else:
-        raise AttributeError(f"module {__name__!r} has no attribute {name!r}")
+@_api.caching_module_getattr  # module-level deprecations
+class __getattr__:
+    IDLE_DELAY = _api.deprecated("3.1", obj_type="", removal="3.6")(property(
+        lambda self: 5))
+    cursord = _api.deprecated("3.5", obj_type="")(property(lambda self: {
+        cursors.MOVE: wx.CURSOR_HAND,
+        cursors.HAND: wx.CURSOR_HAND,
+        cursors.POINTER: wx.CURSOR_ARROW,
+        cursors.SELECT_REGION: wx.CURSOR_CROSS,
+        cursors.WAIT: wx.CURSOR_WAIT,
+        cursors.RESIZE_HORIZONTAL: wx.CURSOR_SIZEWE,
+        cursors.RESIZE_VERTICAL: wx.CURSOR_SIZENS,
+    }))
 
 
 def error_msg_wx(msg, parent=None):
diff --git a/lib/matplotlib/cm.py b/lib/matplotlib/cm.py
index 055a944706ac..0af2f0f327d9 100644
--- a/lib/matplotlib/cm.py
+++ b/lib/matplotlib/cm.py
@@ -16,7 +16,6 @@
 """
 
 from collections.abc import Mapping, MutableMapping
-import functools
 
 import numpy as np
 from numpy import ma
@@ -27,14 +26,11 @@
 from matplotlib._cm_listed import cmaps as cmaps_listed
 
 
-# module-level deprecations.
-@functools.lru_cache(None)
-def __getattr__(name):
-    if name == "LUTSIZE":
-        _api.warn_deprecated("3.5", name=name,
-                             alternative="rcParams['image.lut']")
-        return _LUTSIZE
-    raise AttributeError(f"module {__name__!r} has no attribute {name!r}")
+@_api.caching_module_getattr  # module-level deprecations
+class __getattr__:
+    LUTSIZE = _api.deprecated(
+        "3.5", obj_type="", alternative="rcParams['image.lut']")(
+            property(lambda self: _LUTSIZE))
 
 
 _LUTSIZE = mpl.rcParams['image.lut']
diff --git a/lib/matplotlib/colorbar.py b/lib/matplotlib/colorbar.py
index a056bf69201d..459b14f6c5a7 100644
--- a/lib/matplotlib/colorbar.py
+++ b/lib/matplotlib/colorbar.py
@@ -12,7 +12,6 @@
 """
 
 import copy
-import functools
 import logging
 import textwrap
 
@@ -195,20 +194,14 @@
        _colormap_kw_doc))
 
 
-# module-level deprecations.
-@functools.lru_cache(None)
-def __getattr__(name):
-    if name == "colorbar_doc":
-        _api.warn_deprecated("3.4", name=name)
-        return docstring.interpd.params["colorbar_doc"]
-    elif name == "colormap_kw_doc":
-        _api.warn_deprecated("3.4", name=name)
-        return _colormap_kw_doc
-    elif name == "make_axes_kw_doc":
-        _api.warn_deprecated("3.4", name=name)
-        return _make_axes_param_doc + _make_axes_other_param_doc
-    else:
-        raise AttributeError(f"module {__name__!r} has no attribute {name!r}")
+@_api.caching_module_getattr  # module-level deprecations
+class __getattr__:
+    colorbar_doc = _api.deprecated("3.4", obj_type="")(property(
+        lambda self: docstring.interpd.params["colorbar_doc"]))
+    colorbar_kw_doc = _api.deprecated("3.4", obj_type="")(property(
+        lambda self: _colormap_kw_doc))
+    make_axes_kw_doc = _api.deprecated("3.4", obj_type="")(property(
+        lambda self: _make_axes_param_doc + _make_axes_other_param_doc))
 
 
 def _set_ticks_on_axis_warn(*args, **kw):
diff --git a/lib/matplotlib/style/core.py b/lib/matplotlib/style/core.py
index 65afa0ca8005..85dcc8bc41fe 100644
--- a/lib/matplotlib/style/core.py
+++ b/lib/matplotlib/style/core.py
@@ -12,7 +12,6 @@
 """
 
 import contextlib
-import functools
 import logging
 import os
 from pathlib import Path
@@ -27,13 +26,10 @@
 __all__ = ['use', 'context', 'available', 'library', 'reload_library']
 
 
-# module-level deprecations.
-@functools.lru_cache(None)
-def __getattr__(name):
-    if name == "STYLE_FILE_PATTERN":
-        _api.warn_deprecated("3.5", name=name)
-        return re.compile(r'([\S]+).%s$' % STYLE_EXTENSION)
-    raise AttributeError(f"module {__name__!r} has no attribute {name!r}")
+@_api.caching_module_getattr  # module-level deprecations
+class __getattr__:
+    STYLE_FILE_PATTERN = _api.deprecated("3.5", obj_type="")(property(
+        lambda self: re.compile(r'([\S]+).%s$' % STYLE_EXTENSION)))
 
 
 BASE_LIBRARY_PATH = os.path.join(mpl.get_data_path(), 'stylelib')
diff --git a/lib/matplotlib/tests/test_getattr.py b/lib/matplotlib/tests/test_getattr.py
new file mode 100644
index 000000000000..71556b5b4c71
--- /dev/null
+++ b/lib/matplotlib/tests/test_getattr.py
@@ -0,0 +1,28 @@
+from importlib import import_module
+from pkgutil import walk_packages
+
+import matplotlib
+import pytest
+
+# Get the names of all matplotlib submodules, except for the unit tests.
+module_names = [m.name for m in walk_packages(path=matplotlib.__path__,
+                                              prefix=f'{matplotlib.__name__}.')
+                if not m.name.startswith(__package__)]
+
+
+@pytest.mark.parametrize('module_name', module_names)
+@pytest.mark.filterwarnings('ignore::DeprecationWarning')
+def test_getattr(module_name):
+    """
+    Test that __getattr__ methods raise AttributeError for unknown keys.
+    See #20822, #20855.
+    """
+    try:
+        module = import_module(module_name)
+    except (ImportError, RuntimeError) as e:
+        # Skip modules that cannot be imported due to missing dependencies
+        pytest.skip(f'Cannot import {module_name} due to {e}')
+
+    key = 'THIS_SYMBOL_SHOULD_NOT_EXIST'
+    if hasattr(module, key):
+        delattr(module, key)