diff --git a/lib/matplotlib/tests/test_transforms.py b/lib/matplotlib/tests/test_transforms.py
index ad572fe5287a..75702a608219 100644
--- a/lib/matplotlib/tests/test_transforms.py
+++ b/lib/matplotlib/tests/test_transforms.py
@@ -460,6 +460,12 @@ def assert_bbox_eq(bbox1, bbox2):
     assert_array_equal(bbox1.bounds, bbox2.bounds)
 
 
+def test_bbox_frozen_copies_minpos():
+    bbox = mtransforms.Bbox.from_extents(0.0, 0.0, 1.0, 1.0, minpos=1.0)
+    frozen = bbox.frozen()
+    assert_array_equal(frozen.minpos, bbox.minpos)
+
+
 def test_bbox_intersection():
     bbox_from_ext = mtransforms.Bbox.from_extents
     inter = mtransforms.Bbox.intersection
diff --git a/lib/matplotlib/transforms.py b/lib/matplotlib/transforms.py
index 9a50e4bf0048..e2051a41346b 100644
--- a/lib/matplotlib/transforms.py
+++ b/lib/matplotlib/transforms.py
@@ -807,6 +807,12 @@ def invalidate(self):
             self._check(self._points)
             super().invalidate()
 
+    def frozen(self):
+        # docstring inherited
+        frozen_bbox = super().frozen()
+        frozen_bbox._minpos = self.minpos.copy()
+        return frozen_bbox
+
     @staticmethod
     def unit():
         """Create a new unit `Bbox` from (0, 0) to (1, 1)."""