diff --git a/lib/matplotlib/artist.py b/lib/matplotlib/artist.py
index 6c61be641739..179badd3598e 100644
--- a/lib/matplotlib/artist.py
+++ b/lib/matplotlib/artist.py
@@ -1274,11 +1274,18 @@ def format_cursor_data(self, data):
             # Artist.format_cursor_data would always have precedence over
             # ScalarMappable.format_cursor_data.
             n = self.cmap.N
-            # Midpoints of neighboring color intervals.
-            neighbors = self.norm.inverse(
-                (int(self.norm(data) * n) + np.array([0, 1])) / n)
-            delta = abs(neighbors - data).max()
-            return "[{:-#.{}g}]".format(data, cbook._g_sig_digits(data, delta))
+            if np.ma.getmask(data):
+                return "[]"
+            normed = self.norm(data)
+            if np.isfinite(normed):
+                # Midpoints of neighboring color intervals.
+                neighbors = self.norm.inverse(
+                    (int(self.norm(data) * n) + np.array([0, 1])) / n)
+                delta = abs(neighbors - data).max()
+                g_sig_digits = cbook._g_sig_digits(data, delta)
+            else:
+                g_sig_digits = 3  # Consistent with default below.
+            return "[{:-#.{}g}]".format(data, g_sig_digits)
         else:
             try:
                 data[0]
diff --git a/lib/matplotlib/tests/test_image.py b/lib/matplotlib/tests/test_image.py
index 9aab4e60a7a2..2c4a2763e4c6 100644
--- a/lib/matplotlib/tests/test_image.py
+++ b/lib/matplotlib/tests/test_image.py
@@ -340,6 +340,7 @@ def test_cursor_data():
     "data, text", [
         ([[10001, 10000]], "[10001.000]"),
         ([[.123, .987]], "[0.123]"),
+        ([[np.nan, 1, 2]], "[]"),
     ])
 def test_format_cursor_data(data, text):
     from matplotlib.backend_bases import MouseEvent
@@ -349,7 +350,6 @@ def test_format_cursor_data(data, text):
 
     xdisp, ydisp = ax.transData.transform([0, 0])
     event = MouseEvent('motion_notify_event', fig.canvas, xdisp, ydisp)
-    assert im.get_cursor_data(event) == data[0][0]
     assert im.format_cursor_data(im.get_cursor_data(event)) == text