diff --git a/lib/matplotlib/axes/_base.py b/lib/matplotlib/axes/_base.py
index ecff24540690..5a1ee06d845a 100644
--- a/lib/matplotlib/axes/_base.py
+++ b/lib/matplotlib/axes/_base.py
@@ -2443,6 +2443,20 @@ def _add_text(self, txt):
         self.stale = True
         return txt
 
+    def _point_in_data_domain(self, x, y):
+        """
+        Check if the data point (x, y) is within the valid domain of the axes
+        scales.
+
+        Returns False if the point is outside the data range
+        (e.g. negative coordinates with a log scale).
+        """
+        for val, axis in zip([x, y], self._axis_map.values()):
+            vmin, vmax = axis.limit_range_for_scale(val, val)
+            if vmin != val or vmax != val:
+                return False
+        return True
+
     def _update_line_limits(self, line):
         """
         Figures out the data limit of the given line, updating `.Axes.dataLim`.
diff --git a/lib/matplotlib/tests/test_text.py b/lib/matplotlib/tests/test_text.py
index 551adbedbc61..46231dd70908 100644
--- a/lib/matplotlib/tests/test_text.py
+++ b/lib/matplotlib/tests/test_text.py
@@ -1226,3 +1226,15 @@ def test_ytick_rotation_mode():
         tick.set_rotation(angle)
 
     plt.subplots_adjust(left=0.4, right=0.6, top=.99, bottom=.01)
+
+
+def test_text_tightbbox_outside_scale_domain():
+    # Test that text at positions outside the valid domain of axes scales
+    # (e.g., negative coordinates with log scale) returns a null bbox.
+    fig, ax = plt.subplots()
+    ax.set_yscale('log')
+    ax.set_ylim(1, 100)
+
+    invalid_text = ax.text(0, -5, 'invalid')
+    invalid_bbox = invalid_text.get_tightbbox(fig.canvas.get_renderer())
+    assert not np.isfinite(invalid_bbox.width)
diff --git a/lib/matplotlib/text.py b/lib/matplotlib/text.py
index d794cab1339b..7422affab2cb 100644
--- a/lib/matplotlib/text.py
+++ b/lib/matplotlib/text.py
@@ -1060,6 +1060,15 @@ def get_window_extent(self, renderer=None, dpi=None):
             bbox = bbox.translated(x, y)
             return bbox
 
+    def get_tightbbox(self, renderer=None):
+        # Exclude text at data coordinates outside the valid domain of the axes
+        # scales (e.g., negative coordinates with a log scale).
+        if (self.axes
+                and self.get_transform() == self.axes.transData
+                and not self.axes._point_in_data_domain(*self.get_unitless_position())):
+            return Bbox.null()
+        return super().get_tightbbox(renderer)
+
     def set_backgroundcolor(self, color):
         """
         Set the background color of the text.