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

doc/source/whatsnew/v1.3.0.rst

@@ -294,6 +294,7 @@ Groupby/resample/rolling
 Reshaping
 ^^^^^^^^^
 - Bug in :meth:`DataFrame.unstack` with missing levels led to incorrect index names (:issue:`37510`)
+- Bug in :func:`join` over :class:`MultiIndex` returned wrong result, when one of both indexes had only one level (:issue:`36909`)
 - Bug in :func:`concat` incorrectly casting to ``object`` dtype in some cases when one or more of the operands is empty (:issue:`38843`)
 -
 

pandas/core/indexes/base.py

@@ -1672,7 +1672,7 @@ def _drop_level_numbers(self, levnums: List[int]):
         Drop MultiIndex levels by level _number_, not name.
         """
 
-        if not levnums:
+        if not levnums and (len(self) > 1 or not isinstance(self, ABCMultiIndex)):
             return self
         if len(levnums) >= self.nlevels:
             raise ValueError(

pandas/tests/indexes/multi/test_drop.py

@@ -180,3 +180,11 @@ def test_single_level_drop_partially_missing_elements():
     msg = r"labels \['a'\] not found in level"
     with pytest.raises(KeyError, match=msg):
         mi.drop([np.nan, 1, "a"], level=0)
+
+
+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

@@ -815,3 +815,20 @@ def test_join_cross(input_col, output_cols):
     result = left.join(right, how="cross", lsuffix="_x", rsuffix="_y")
     expected = DataFrame({output_cols[0]: [1, 1, 3, 3], output_cols[1]: [3, 4, 3, 4]})
     tm.assert_frame_equal(result, expected)
+
+
+@pytest.mark.parametrize("how", ["left", "right", "inner", "outer"])
+def test_join_multiindex_one_level(how):
+    # GH#36909
+    left = DataFrame(
+        data={"c": 3}, index=pd.MultiIndex.from_tuples([(1, 2)], names=("a", "b"))
+    )
+    right = DataFrame(
+        data={"d": 4}, index=pd.MultiIndex.from_tuples([(2,)], names=("b",))
+    )
+    result = left.join(right, how=how)
+    expected = DataFrame(
+        {"c": [3], "d": [4]},
+        index=pd.MultiIndex.from_tuples([(2, 1)], names=["b", "a"]),
+    )
+    tm.assert_frame_equal(result, expected)