diff --git a/lib/matplotlib/tests/test_text.py b/lib/matplotlib/tests/test_text.py
index c26edeb55abd..10685f62db85 100644
--- a/lib/matplotlib/tests/test_text.py
+++ b/lib/matplotlib/tests/test_text.py
@@ -6,6 +6,7 @@
 import pytest
 
 import matplotlib
+from matplotlib.backend_bases import MouseEvent
 import matplotlib.patches as mpatches
 import matplotlib.pyplot as plt
 from matplotlib.testing.decorators import image_comparison
@@ -204,13 +205,10 @@ def test_afm_kerning():
 
 @image_comparison(baseline_images=['text_contains'], extensions=['png'])
 def test_contains():
-    import matplotlib.backend_bases as mbackend
-
     fig = plt.figure()
     ax = plt.axes()
 
-    mevent = mbackend.MouseEvent(
-        'button_press_event', fig.canvas, 0.5, 0.5, 1, None)
+    mevent = MouseEvent('button_press_event', fig.canvas, 0.5, 0.5, 1, None)
 
     xs = np.linspace(0.25, 0.75, 30)
     ys = np.linspace(0.25, 0.75, 30)
@@ -236,6 +234,19 @@ def test_contains():
         ax.viewLim.set(vl)
 
 
+def test_annotation_contains():
+    # Check that Annotation.contains looks at the bboxes of the text and the
+    # arrow separately, not at the joint bbox.
+    fig, ax = plt.subplots()
+    ann = ax.annotate(
+        "hello", xy=(.4, .4), xytext=(.6, .6), arrowprops={"arrowstyle": "->"})
+    fig.canvas.draw()   # Needed for the same reason as in test_contains.
+    event = MouseEvent(
+        "button_press_event", fig.canvas,
+        *ax.transData.transform_point((.5, .6)))
+    assert ann.contains(event) == (False, {})
+
+
 @image_comparison(baseline_images=['titles'])
 def test_titles():
     # left and right side titles
diff --git a/lib/matplotlib/text.py b/lib/matplotlib/text.py
index b5a3567dfe70..8450b60d0891 100644
--- a/lib/matplotlib/text.py
+++ b/lib/matplotlib/text.py
@@ -200,7 +200,10 @@ def contains(self, mouseevent):
         if not self.get_visible() or self._renderer is None:
             return False, {}
 
-        l, b, w, h = self.get_window_extent().bounds
+        # Explicitly use Text.get_window_extent(self) and not
+        # self.get_window_extent() so that Annotation.contains does not
+        # accidentally cover the entire annotation bounding box.
+        l, b, w, h = Text.get_window_extent(self).bounds
         r, t = l + w, b + h
 
         x, y = mouseevent.x, mouseevent.y
@@ -2187,11 +2190,12 @@ def transform(renderer) -> Transform
             self.arrow_patch = None
 
     def contains(self, event):
+        if self._contains is not None:
+            return self._contains(self, event)
         contains, tinfo = Text.contains(self, event)
         if self.arrow_patch is not None:
             in_patch, _ = self.arrow_patch.contains(event)
             contains = contains or in_patch
-
         return contains, tinfo
 
     @property