Fix regression for is_monotonic_increasing with nan in MultiIndex

doc/source/whatsnew/v1.1.4.rst

@@ -20,6 +20,7 @@ Fixed regressions
 - Fixed regression in :class:`RollingGroupby` with ``sort=False`` not being respected (:issue:`36889`)
 - Fixed regression in :meth:`Series.astype` converting ``None`` to ``"nan"`` when casting to string (:issue:`36904`)
 - Fixed regression in :class:`RollingGroupby` causing a segmentation fault with Index of dtype object (:issue:`36727`)
+- Fixed regression in :attr:`MultiIndex.is_monotonic_increasing` returning wrong results with ``"nan"`` in at least one of the levels (:issue:`37220`)
 
 .. ---------------------------------------------------------------------------
 

pandas/core/indexes/multi.py

@@ -1539,7 +1539,10 @@ def is_monotonic_increasing(self) -> bool:
         return if the index is monotonic increasing (only equal or
         increasing) values.
         """
-        if all(x.is_monotonic for x in self.levels):
+        if all(
+            level.is_monotonic and -1 not in code
+            for (level, code) in zip(self.levels, self.codes)
+        ):
             # If each level is sorted, we can operate on the codes directly. GH27495
             return libalgos.is_lexsorted(
                 [x.astype("int64", copy=False) for x in self.codes]

pandas/tests/indexes/multi/test_monotonic.py

@@ -174,3 +174,9 @@ def test_is_strictly_monotonic_decreasing():
     )
     assert idx.is_monotonic_decreasing is True
     assert idx._is_strictly_monotonic_decreasing is False
+
+
+def test_is_monotonic_with_nans():
+    # GH: 37220
+    idx = pd.MultiIndex.from_tuples([(np.nan,), (1,)], names=["test"])
+    assert idx.is_monotonic_increasing is False