diff --git a/doc/source/whatsnew/v0.20.3.txt b/doc/source/whatsnew/v0.20.3.txt
index b2d382a3202a5..c4768f980bc6a 100644
--- a/doc/source/whatsnew/v0.20.3.txt
+++ b/doc/source/whatsnew/v0.20.3.txt
@@ -39,7 +39,7 @@ Bug Fixes
 - Fixed issue with dataframe scatter plot for categorical data that reports incorrect column key not found when categorical data is used for plotting (:issue:`16199`)
 - Fixed a pytest marker failing downstream packages' tests suites (:issue:`16680`)
 - Fixed compat with loading a ``DataFrame`` with a ``PeriodIndex``, from a ``format='fixed'`` HDFStore, in Python 3, that was written in Python 2 (:issue:`16781`)
-
+- Fixed bug where computing the rolling covariance of a MultiIndexed ``DataFrame`` improperly raised a ``ValueError`` (:issue:`16789`)
 
 Conversion
 ^^^^^^^^^^
diff --git a/pandas/core/window.py b/pandas/core/window.py
index 01b1bdc3e5054..1e16eff7d56cc 100644
--- a/pandas/core/window.py
+++ b/pandas/core/window.py
@@ -1948,7 +1948,7 @@ def dataframe_from_int_dict(data, frame_template):
                 result.columns = Index(result.columns).set_names(
                     arg2.columns.name)
                 result.index = result.index.set_names(
-                    [arg1.index.name, arg1.columns.name])
+                    arg1.index.names + arg1.columns.names)
 
                 return result
 
diff --git a/pandas/tests/indexes/test_multi.py b/pandas/tests/indexes/test_multi.py
index ef8806246c2c5..03f90b25415bb 100644
--- a/pandas/tests/indexes/test_multi.py
+++ b/pandas/tests/indexes/test_multi.py
@@ -61,6 +61,15 @@ def f():
 
         tm.assert_raises_regex(ValueError, 'The truth value of a', f)
 
+    def test_multi_index_names(self):
+
+        # GH 16789
+        cols = pd.MultiIndex.from_product([['A', 'B'], ['C', 'D', 'E']],
+                                          names=['1', '2'])
+        df = pd.DataFrame(np.ones((10, 6)), columns=cols)
+        rolling_result = df.rolling(3).cov()
+        assert rolling_result.index.names == [None, '1', '2']
+
     def test_labels_dtypes(self):
 
         # GH 8456