diff --git a/lib/matplotlib/axes/_base.py b/lib/matplotlib/axes/_base.py
index 0acba3e6044b..26d8df32e396 100644
--- a/lib/matplotlib/axes/_base.py
+++ b/lib/matplotlib/axes/_base.py
@@ -2440,6 +2440,16 @@ def handle_single_axis(scale, autoscaleon, shared_axes, interval,
                 dl.extend(y_finite)
 
             bb = mtransforms.BboxBase.union(dl)
+            # fall back on the viewlimits if this is not finite:
+            vl = None
+            if not np.isfinite(bb.intervalx).all():
+                vl = mtransforms.BboxBase.union([ax.viewLim for ax in shared])
+                bb.intervalx = vl.intervalx
+            if not np.isfinite(bb.intervaly).all():
+                if vl is None:
+                    vl = mtransforms.BboxBase.union(
+                        [ax.viewLim for ax in shared])
+                bb.intervaly = vl.intervaly
             x0, x1 = getattr(bb, interval)
             locator = axis.get_major_locator()
             x0, x1 = locator.nonsingular(x0, x1)
diff --git a/lib/matplotlib/tests/test_axes.py b/lib/matplotlib/tests/test_axes.py
index 8a46794ad304..9109740d415f 100644
--- a/lib/matplotlib/tests/test_axes.py
+++ b/lib/matplotlib/tests/test_axes.py
@@ -6296,3 +6296,16 @@ def test_axis_bool_arguments(fig_test, fig_ref):
     ax.axis(False)
     ax.axis(True)
     fig_ref.add_subplot(212).axis("on")
+
+
+def test_datetime_masked():
+    # make sure that all-masked data falls back to the viewlim
+    # set in convert.axisinfo....
+    x = np.array([datetime.datetime(2017, 1, n) for n in range(1, 6)])
+    y = np.array([1, 2, 3, 4, 5])
+    m = np.ma.masked_greater(y, 0)
+
+    fig, ax = plt.subplots()
+    ax.plot(x, m)
+    # these are the default viewlim
+    assert ax.get_xlim() == (730120.0, 733773.0)