diff --git a/lib/matplotlib/projections/polar.py b/lib/matplotlib/projections/polar.py
@@ -422,14 +422,25 @@ def __call__(self):
                     return [tick for tick in self.base() if tick > rorigin]
         return self.base()
 
+    def _zero_in_bounds(self):
+        """
+        Return True if zero is within the valid values for the
+        scale of the radial axis.
+        """
+        vmin, vmax = self._axes.yaxis._scale.limit_range_for_scale(0, 1, 1e-5)
+        return vmin == 0
+
     def nonsingular(self, vmin, vmax):
         # docstring inherited
-        return ((0, 1) if (vmin, vmax) == (-np.inf, np.inf)  # Init. limits.
-                else self.base.nonsingular(vmin, vmax))
+        if self._zero_in_bounds() and (vmin, vmax) == (-np.inf, np.inf):
+            # Initial view limits
+            return (0, 1)
+        else:
+            return self.base.nonsingular(vmin, vmax)
 
     def view_limits(self, vmin, vmax):
         vmin, vmax = self.base.view_limits(vmin, vmax)
-        if vmax > vmin:
+        if self._zero_in_bounds() and vmax > vmin:
             # this allows inverted r/y-lims
             vmin = min(0, vmin)
         return mtransforms.nonsingular(vmin, vmax)

diff --git a/lib/matplotlib/tests/test_polar.py b/lib/matplotlib/tests/test_polar.py
@@ -291,6 +291,13 @@ def test_polar_no_data():
     assert ax.get_rmin() == 0 and ax.get_rmax() == 1
 
 
+def test_polar_default_log_lims():
+    plt.subplot(projection='polar')
+    ax = plt.gca()
+    ax.set_rscale('log')
+    assert ax.get_rmin() > 0
+
+
 def test_polar_not_datalim_adjustable():
     ax = plt.figure().add_subplot(projection="polar")
     with pytest.raises(ValueError):