diff --git a/lib/matplotlib/axes/_base.py b/lib/matplotlib/axes/_base.py
index e6b368d0117a..6981cbef280c 100644
--- a/lib/matplotlib/axes/_base.py
+++ b/lib/matplotlib/axes/_base.py
@@ -4259,7 +4259,9 @@ def get_tightbbox(self, renderer, call_axes_locator=True,
 
         for a in bbox_artists:
             bbox = a.get_tightbbox(renderer)
-            if bbox is not None and (bbox.width != 0 or bbox.height != 0):
+            if (bbox is not None and
+                    (bbox.width != 0 or bbox.height != 0) and
+                    np.isfinite(bbox.width) and np.isfinite(bbox.height)):
                 bb.append(bbox)
 
         _bbox = mtransforms.Bbox.union(
diff --git a/lib/matplotlib/tests/test_axes.py b/lib/matplotlib/tests/test_axes.py
index b4879e3b208a..08bff9272930 100644
--- a/lib/matplotlib/tests/test_axes.py
+++ b/lib/matplotlib/tests/test_axes.py
@@ -5849,3 +5849,10 @@ class DummySubplot(matplotlib.axes.SubplotBase, Dummy):
     FactoryDummySubplot = matplotlib.axes.subplot_class_factory(Dummy)
 
     assert DummySubplot is FactoryDummySubplot
+
+
+def test_gettightbbox_ignoreNaN():
+    fig, ax = plt.subplots()
+    t = ax.text(np.NaN, 1, 'Boo')
+    renderer = fig.canvas.get_renderer()
+    np.testing.assert_allclose(ax.get_tightbbox(renderer).width, 532.444444)