BUG: Join did not work correctly when one MultiIndex had only one level

doc/source/whatsnew/v1.2.0.rst

@@ -474,6 +474,7 @@ Reshaping
 - Bug in func :meth:`crosstab` when using multiple columns with ``margins=True`` and ``normalize=True`` (:issue:`35144`)
 - Bug in :meth:`DataFrame.agg` with ``func={'name':<FUNC>}`` incorrectly raising ``TypeError`` when ``DataFrame.columns==['Name']`` (:issue:`36212`)
 - Bug in :meth:`Series.transform` would give incorrect results or raise when the argument ``func`` was dictionary (:issue:`35811`)
+- Bug in :func:`join` over :class:`MultiIndex` returned wrong result, when one of both indexes had only one level (:issue:`36909`)
 -
 
 Sparse

pandas/core/indexes/base.py

@@ -1552,7 +1552,7 @@ def droplevel(self, level=0):
 
         levnums = sorted(self._get_level_number(lev) for lev in level)[::-1]
 
-        if len(level) == 0:
+        if len(level) == 0 and (len(self) > 1 or not isinstance(self, ABCMultiIndex)):
             return self
         if len(level) >= self.nlevels:
             raise ValueError(

pandas/tests/indexes/multi/test_drop.py

@@ -139,3 +139,11 @@ def test_drop_not_lexsorted():
     tm.assert_index_equal(lexsorted_mi, not_lexsorted_mi)
     with tm.assert_produces_warning(PerformanceWarning):
         tm.assert_index_equal(lexsorted_mi.drop("a"), not_lexsorted_mi.drop("a"))
+
+
+def test_droplevel_multiindex_one_level():
+    # GH: 37208
+    index = pd.MultiIndex.from_tuples([(2,)], names=("b",))
+    result = index.droplevel([])
+    expected = pd.Int64Index([2], name="b")
+    tm.assert_index_equal(result, expected)

pandas/tests/reshape/merge/test_join.py

@@ -879,3 +879,20 @@ def _join_by_hand(a, b, how="left"):
     for col, s in b_re.items():
         a_re[col] = s
     return a_re.reindex(columns=result_columns)
+
+
+@pytest.mark.parametrize("how", ["left", "right", "inner", "outer"])
+def test_join_multiindex_one_level(how):
+    # GH: 36909
+    left = pd.DataFrame(
+        data={"c": 3}, index=pd.MultiIndex.from_tuples([(1, 2)], names=("a", "b"))
+    )
+    right = pd.DataFrame(
+        data={"d": 4}, index=pd.MultiIndex.from_tuples([(2,)], names=("b",))
+    )
+    result = left.join(right, how=how)
+    expected = pd.DataFrame(
+        {"c": [3], "d": [4]},
+        index=pd.MultiIndex.from_tuples([(2, 1)], names=["b", "a"]),
+    )
+    tm.assert_frame_equal(result, expected)