diff --git a/lib/matplotlib/transforms.py b/lib/matplotlib/transforms.py
index 000bb38befd1..936455acd6c5 100644
--- a/lib/matplotlib/transforms.py
+++ b/lib/matplotlib/transforms.py
@@ -645,14 +645,16 @@ def splity(self, *args):
     def count_contains(self, vertices):
         """
         Count the number of vertices contained in the :class:`Bbox`.
+        Any vertices with a non-finite x or y value are ignored.
 
         *vertices* is a Nx2 Numpy array.
         """
         if len(vertices) == 0:
             return 0
         vertices = np.asarray(vertices)
-        return (
-            ((self.min < vertices) & (vertices < self.max)).all(axis=1).sum())
+        with np.errstate(invalid='ignore'):
+            return (((self.min < vertices) &
+                     (vertices < self.max)).all(axis=1).sum())
 
     def count_overlaps(self, bboxes):
         """