diff --git a/doc/source/whatsnew/v1.0.0.rst b/doc/source/whatsnew/v1.0.0.rst
index efea1fc1f525f..6804cc08a0638 100755
--- a/doc/source/whatsnew/v1.0.0.rst
+++ b/doc/source/whatsnew/v1.0.0.rst
@@ -946,6 +946,7 @@ Reshaping
 - :func:`qcut` and :func:`cut` now handle boolean input (:issue:`20303`)
 - Fix to ensure all int dtypes can be used in :func:`merge_asof` when using a tolerance value. Previously every non-int64 type would raise an erroneous ``MergeError`` (:issue:`28870`).
 - Better error message in :func:`get_dummies` when `columns` isn't a list-like value (:issue:`28383`)
+- Bug in :meth:`Index.join` that caused infinite recursion error for mismatched ``MultiIndex`` name orders. (:issue:`25760`, :issue:`28956`)
 - Bug :meth:`Series.pct_change` where supplying an anchored frequency would throw a ValueError (:issue:`28664`)
 - Bug where :meth:`DataFrame.equals` returned True incorrectly in some cases when two DataFrames had the same columns in different orders (:issue:`28839`)
 - Bug in :meth:`DataFrame.replace` that caused non-numeric replacer's dtype not respected (:issue:`26632`)
diff --git a/pandas/core/indexes/base.py b/pandas/core/indexes/base.py
index e9e3a5ef94a1f..28e144a957d1c 100644
--- a/pandas/core/indexes/base.py
+++ b/pandas/core/indexes/base.py
@@ -3368,8 +3368,13 @@ def _join_multi(self, other, how, return_indexers=True):
             ldrop_names = list(self_names - overlap)
             rdrop_names = list(other_names - overlap)
 
-            self_jnlevels = self.droplevel(ldrop_names)
-            other_jnlevels = other.droplevel(rdrop_names)
+            # if only the order differs
+            if not len(ldrop_names + rdrop_names):
+                self_jnlevels = self
+                other_jnlevels = other.reorder_levels(self.names)
+            else:
+                self_jnlevels = self.droplevel(ldrop_names)
+                other_jnlevels = other.droplevel(rdrop_names)
 
             # Join left and right
             # Join on same leveled multi-index frames is supported
diff --git a/pandas/tests/indexes/multi/test_join.py b/pandas/tests/indexes/multi/test_join.py
index 42d8cf761842e..31ab521958342 100644
--- a/pandas/tests/indexes/multi/test_join.py
+++ b/pandas/tests/indexes/multi/test_join.py
@@ -87,3 +87,19 @@ def test_join_self_unique(idx, join_type):
     if idx.is_unique:
         joined = idx.join(idx, how=join_type)
         assert (idx == joined).all()
+
+
+def test_join_multi_wrong_order():
+    # GH 25760
+    # GH 28956
+
+    midx1 = pd.MultiIndex.from_product([[1, 2], [3, 4]], names=["a", "b"])
+    midx2 = pd.MultiIndex.from_product([[1, 2], [3, 4]], names=["b", "a"])
+
+    join_idx, lidx, ridx = midx1.join(midx2, return_indexers=False)
+
+    exp_ridx = np.array([-1, -1, -1, -1], dtype=np.intp)
+
+    tm.assert_index_equal(midx1, join_idx)
+    assert lidx is None
+    tm.assert_numpy_array_equal(ridx, exp_ridx)
diff --git a/pandas/tests/reshape/merge/test_multi.py b/pandas/tests/reshape/merge/test_multi.py
index bce62571d55ec..d269196401554 100644
--- a/pandas/tests/reshape/merge/test_multi.py
+++ b/pandas/tests/reshape/merge/test_multi.py
@@ -828,3 +828,22 @@ def test_single_common_level(self):
         ).set_index(["key", "X", "Y"])
 
         tm.assert_frame_equal(result, expected)
+
+    def test_join_multi_wrong_order(self):
+        # GH 25760
+        # GH 28956
+
+        midx1 = pd.MultiIndex.from_product([[1, 2], [3, 4]], names=["a", "b"])
+        midx3 = pd.MultiIndex.from_tuples([(4, 1), (3, 2), (3, 1)], names=["b", "a"])
+
+        left = pd.DataFrame(index=midx1, data={"x": [10, 20, 30, 40]})
+        right = pd.DataFrame(index=midx3, data={"y": ["foo", "bar", "fing"]})
+
+        result = left.join(right)
+
+        expected = pd.DataFrame(
+            index=midx1,
+            data={"x": [10, 20, 30, 40], "y": ["fing", "foo", "bar", np.nan]},
+        )
+
+        tm.assert_frame_equal(result, expected)