diff --git a/doc/source/whatsnew/v0.23.2.txt b/doc/source/whatsnew/v0.23.2.txt
index 3e4326dea2ecc..0d3f9cb8dd3b6 100644
--- a/doc/source/whatsnew/v0.23.2.txt
+++ b/doc/source/whatsnew/v0.23.2.txt
@@ -52,6 +52,7 @@ Bug Fixes
 **Indexing**
 
 - Bug in :meth:`Index.get_indexer_non_unique` with categorical key (:issue:`21448`)
+- Bug in comparison operations for :class:`MultiIndex` where error was raised on equality / inequality comparison involving a MultiIndex with ``nlevels == 1`` (:issue:`21149`)
 -
 
 **I/O**
diff --git a/pandas/core/indexes/base.py b/pandas/core/indexes/base.py
index 36345a32a3bf7..4b32e5d4f5654 100644
--- a/pandas/core/indexes/base.py
+++ b/pandas/core/indexes/base.py
@@ -91,7 +91,8 @@ def cmp_method(self, other):
         if needs_i8_conversion(self) and needs_i8_conversion(other):
             return self._evaluate_compare(other, op)
 
-        if is_object_dtype(self) and self.nlevels == 1:
+        from .multi import MultiIndex
+        if is_object_dtype(self) and not isinstance(self, MultiIndex):
             # don't pass MultiIndex
             with np.errstate(all='ignore'):
                 result = ops._comp_method_OBJECT_ARRAY(op, self.values, other)
diff --git a/pandas/tests/indexes/test_multi.py b/pandas/tests/indexes/test_multi.py
index 0ab3447909d9b..ab53002ee1587 100644
--- a/pandas/tests/indexes/test_multi.py
+++ b/pandas/tests/indexes/test_multi.py
@@ -3307,3 +3307,20 @@ def test_duplicate_multiindex_labels(self):
         with pytest.raises(ValueError):
             ind.set_levels([['A', 'B', 'A', 'A', 'B'], [2, 1, 3, -2, 5]],
                            inplace=True)
+
+    def test_multiindex_compare(self):
+        # GH 21149
+        # Ensure comparison operations for MultiIndex with nlevels == 1
+        # behave consistently with those for MultiIndex with nlevels > 1
+
+        midx = pd.MultiIndex.from_product([[0, 1]])
+
+        # Equality self-test: MultiIndex object vs self
+        expected = pd.Series([True, True])
+        result = pd.Series(midx == midx)
+        tm.assert_series_equal(result, expected)
+
+        # Greater than comparison: MultiIndex object vs self
+        expected = pd.Series([False, False])
+        result = pd.Series(midx > midx)
+        tm.assert_series_equal(result, expected)