Fix regression for is_monotonic_increasing with nan in MultiIndex

doc/source/whatsnew/v1.1.4.rst

@@ -23,6 +23,7 @@ Fixed regressions
 - Fixed regression in :meth:`DataFrame.resample(...).apply(...)` raised ``AttributeError`` when input was a :class:`DataFrame` and only a :class:`Series` was evaluated (:issue:`36951`)
 - Fixed regression in :class:`PeriodDtype` comparing both equal and unequal to its string representation (:issue:`37265`)
 - Fixed regression in certain offsets (:meth:`pd.offsets.Day() <pandas.tseries.offsets.Day>` and below) no longer being hashable (:issue:`37267`)
+- 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 any(-1 in code for code in self.codes):
+            return False
+
+        if all(level.is_monotonic for level in self.levels):
             # 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

@@ -1,4 +1,5 @@
 import numpy as np
+import pytest
 
 import pandas as pd
 from pandas import Index, MultiIndex
@@ -174,3 +175,14 @@ def test_is_strictly_monotonic_decreasing():
     )
     assert idx.is_monotonic_decreasing is True
     assert idx._is_strictly_monotonic_decreasing is False
+
+
+@pytest.mark.parametrize("attr", ["is_monotonic_increasing", "is_monotonic_decreasing"])
+@pytest.mark.parametrize(
+    "values",
+    [[(np.nan,), (1,), (2,)], [(1,), (np.nan,), (2,)], [(1,), (2,), (np.nan,)]],
+)
+def test_is_monotonic_with_nans(values, attr):
+    # GH: 37220
+    idx = pd.MultiIndex.from_tuples(values, names=["test"])
+    assert getattr(idx, attr) is False