diff --git a/lib/matplotlib/axes/_base.py b/lib/matplotlib/axes/_base.py
index 045e68925766..282517cba817 100644
--- a/lib/matplotlib/axes/_base.py
+++ b/lib/matplotlib/axes/_base.py
@@ -2539,25 +2539,20 @@ def handle_single_axis(scale, autoscaleon, shared_axes, interval,
                 return  # nothing to do...
 
             shared = shared_axes.get_siblings(self)
-            dl = [ax.dataLim for ax in shared]
-            # ignore non-finite data limits if good limits exist
-            finite_dl = [d for d in dl if np.isfinite(d).all()]
-            if len(finite_dl):
-                # if finite limits exist for at least one axis (and the
-                # other is infinite), restore the finite limits
-                x_finite = [d for d in dl
-                            if (np.isfinite(d.intervalx).all() and
-                                (d not in finite_dl))]
-                y_finite = [d for d in dl
-                            if (np.isfinite(d.intervaly).all() and
-                                (d not in finite_dl))]
-
-                dl = finite_dl
-                dl.extend(x_finite)
-                dl.extend(y_finite)
-
-            bb = mtransforms.BboxBase.union(dl)
-            x0, x1 = getattr(bb, interval)
+            # Base autoscaling on finite data limits when there is at least one
+            # finite data limit among all the shared_axes and intervals.
+            # Also, find the minimum minpos for use in the margin calculation.
+            x_values = []
+            minimum_minpos = np.inf
+            for ax in shared:
+                x_values.extend(getattr(ax.dataLim, interval))
+                minimum_minpos = min(minimum_minpos,
+                                     getattr(ax.dataLim, minpos))
+            x_values = np.extract(np.isfinite(x_values), x_values)
+            if x_values.size >= 1:
+                x0, x1 = (x_values.min(), x_values.max())
+            else:
+                x0, x1 = (-np.inf, np.inf)
             # If x0 and x1 are non finite, use the locator to figure out
             # default limits.
             locator = axis.get_major_locator()
@@ -2578,10 +2573,9 @@ def handle_single_axis(scale, autoscaleon, shared_axes, interval,
 
             # Add the margin in figure space and then transform back, to handle
             # non-linear scales.
-            minpos = getattr(bb, minpos)
             transform = axis.get_transform()
             inverse_trans = transform.inverted()
-            x0, x1 = axis._scale.limit_range_for_scale(x0, x1, minpos)
+            x0, x1 = axis._scale.limit_range_for_scale(x0, x1, minimum_minpos)
             x0t, x1t = transform.transform([x0, x1])
             delta = (x1t - x0t) * margin
             if not np.isfinite(delta):
diff --git a/lib/matplotlib/tests/test_axes.py b/lib/matplotlib/tests/test_axes.py
index 84b13405af33..45fdcf5d6182 100644
--- a/lib/matplotlib/tests/test_axes.py
+++ b/lib/matplotlib/tests/test_axes.py
@@ -6480,3 +6480,12 @@ def test_relative_ticklabel_sizes(size):
     for name, axis in zip(['x', 'y'], [ax.xaxis, ax.yaxis]):
         for tick in axis.get_major_ticks():
             assert tick.label1.get_size() == axis._get_tick_label_size(name)
+
+
+def test_multiplot_autoscale():
+    fig = plt.figure()
+    ax1, ax2 = fig.subplots(2, 1, sharex='all')
+    ax1.scatter([1, 2, 3, 4], [2, 3, 2, 3])
+    ax2.axhspan(-5, 5)
+    xlim = ax1.get_xlim()
+    assert np.allclose(xlim, [0.5, 4.5])