diff --git a/pandas/core/indexes/base.py b/pandas/core/indexes/base.py
index 04617926ae110..e556dc5f970eb 100644
--- a/pandas/core/indexes/base.py
+++ b/pandas/core/indexes/base.py
@@ -4192,8 +4192,7 @@ def dispatch_missing(op, left, right, result):
         result = missing.fill_zeros(result, left, right,
                                     opstr, np.nan)
     elif op is divmod:
-        res0 = missing.fill_zeros(result[0], left, right,
-                                  opstr, np.nan)
+        res0 = missing.mask_zero_div_zero(left, right, result[0])
         res1 = missing.fill_zeros(result[1], left, right,
                                   opstr, np.nan)
         result = (res0, res1)
diff --git a/pandas/tests/indexes/test_numeric.py b/pandas/tests/indexes/test_numeric.py
index d3c80d5cec20a..67fa76cf92152 100644
--- a/pandas/tests/indexes/test_numeric.py
+++ b/pandas/tests/indexes/test_numeric.py
@@ -197,6 +197,19 @@ def test_mod_zero(self, zero):
         ser_compat = Series(idx).astype('i8') % np.array(zero).astype('i8')
         tm.assert_series_equal(ser_compat, Series(result))
 
+    @pytest.mark.parametrize('zero', zeros)
+    def test_divmod_zero(self, zero):
+        idx = self.create_index()
+
+        exleft = Index([np.nan, np.inf, np.inf, np.inf, np.inf],
+                       dtype=np.float64)
+        exright = Index([np.nan, np.nan, np.nan, np.nan, np.nan],
+                        dtype=np.float64)
+
+        result = divmod(idx, zero)
+        tm.assert_index_equal(result[0], exleft)
+        tm.assert_index_equal(result[1], exright)
+
     def test_explicit_conversions(self):
 
         # GH 8608