diff --git a/lib/mpl_toolkits/mplot3d/art3d.py b/lib/mpl_toolkits/mplot3d/art3d.py
index 8b0669775eaf..f206213e9d65 100644
--- a/lib/mpl_toolkits/mplot3d/art3d.py
+++ b/lib/mpl_toolkits/mplot3d/art3d.py
@@ -737,6 +737,18 @@ def set_zsort(self, zsort):
         self._sort_zpos = None
         self.stale = True
 
+    def _zsortval(self, zs):
+        """
+        Compute the value to use for z-sorting given the viewer z
+        coordinates of an object `zs`, with larger values drawn underneath
+        smaller values.
+
+        This function should never return `nan`, and returns `np.inf` if no
+        non-nan value is computable.
+        """
+        nans = np.isnan(zs)
+        return np.inf if nans.all() else self._zsortfunc(zs[~nans])
+
     def get_vector(self, segments3d):
         """Optimize points for projection."""
         if len(segments3d):
@@ -815,7 +827,7 @@ def do_3d_projection(self, renderer=None):
         if xyzlist:
             # sort by depth (furthest drawn first)
             z_segments_2d = sorted(
-                ((self._zsortfunc(zs), np.column_stack([xs, ys]), fc, ec, idx)
+                ((self._zsortval(zs), np.column_stack([xs, ys]), fc, ec, idx)
                  for idx, ((xs, ys, zs), fc, ec)
                  in enumerate(zip(xyzlist, cface, cedge))),
                 key=lambda x: x[0], reverse=True)