diff --git a/lib/matplotlib/figure.py b/lib/matplotlib/figure.py
index f86c0c78936c..0872f10247e8 100644
--- a/lib/matplotlib/figure.py
+++ b/lib/matplotlib/figure.py
@@ -2366,11 +2366,14 @@ def get_tightbbox(self, renderer, bbox_extra_artists=None):
                 except TypeError:
                     bbox = ax.get_tightbbox(renderer)
                 bb.append(bbox)
+        bb = [b for b in bb
+              if (np.isfinite(b.width) and np.isfinite(b.height)
+                  and (b.width != 0 or b.height != 0))]
 
         if len(bb) == 0:
             return self.bbox_inches
 
-        _bbox = Bbox.union([b for b in bb if b.width != 0 or b.height != 0])
+        _bbox = Bbox.union(bb)
 
         bbox_inches = TransformedBbox(_bbox,
                                       Affine2D().scale(1. / self.dpi))
diff --git a/lib/matplotlib/tests/test_bbox_tight.py b/lib/matplotlib/tests/test_bbox_tight.py
index 46f37632e944..8c99c4572f76 100644
--- a/lib/matplotlib/tests/test_bbox_tight.py
+++ b/lib/matplotlib/tests/test_bbox_tight.py
@@ -1,4 +1,5 @@
 import numpy as np
+from io import BytesIO
 
 from matplotlib.testing.decorators import image_comparison
 import matplotlib.pyplot as plt
@@ -86,3 +87,12 @@ def test_bbox_inches_tight_raster():
     fig = plt.figure()
     ax = fig.add_subplot(111)
     ax.plot([1.0, 2.0], rasterized=True)
+
+
+def test_only_on_non_finite_bbox():
+
+    fig, ax = plt.subplots()
+    ax.annotate("", xy=(0, float('nan')))
+    ax.set_axis_off()
+    # we only need to test that it does not error out on save
+    fig.savefig(BytesIO(), bbox_inches='tight', format='png')