diff --git a/doc/source/whatsnew/v1.4.0.rst b/doc/source/whatsnew/v1.4.0.rst
index f55d66ccaa5a9..ca24055e85ee4 100644
--- a/doc/source/whatsnew/v1.4.0.rst
+++ b/doc/source/whatsnew/v1.4.0.rst
@@ -291,7 +291,7 @@ Performance improvements
 - Performance improvement in :func:`read_stata` (:issue:`43059`)
 - Performance improvement in :meth:`to_datetime` with ``uint`` dtypes (:issue:`42606`)
 - Performance improvement in :meth:`Series.sparse.to_coo` (:issue:`42880`)
--
+- Performance improvement in indexing with a :class:`MultiIndex` indexer on another :class:`MultiIndex` (:issue:43370`)
 
 .. ---------------------------------------------------------------------------
 
diff --git a/pandas/_libs/index.pyi b/pandas/_libs/index.pyi
index 8b09c3771d070..c4a695acc2768 100644
--- a/pandas/_libs/index.pyi
+++ b/pandas/_libs/index.pyi
@@ -2,6 +2,8 @@ import numpy as np
 
 from pandas._typing import npt
 
+from pandas import MultiIndex
+
 class IndexEngine:
     over_size_threshold: bool
     def __init__(self, vgetter, n: int): ...
@@ -59,7 +61,7 @@ class BaseMultiIndexCodesEngine:
         self,
         target: npt.NDArray[np.object_],
     ) -> npt.NDArray[np.intp]: ...
-    def _extract_level_codes(self, target: object): ...
+    def _extract_level_codes(self, target: MultiIndex) -> np.ndarray: ...
     def get_indexer_with_fill(
         self,
         target: np.ndarray,  # np.ndarray[object] of tuples
diff --git a/pandas/_libs/index.pyx b/pandas/_libs/index.pyx
index b72be00714b6c..7aff683173855 100644
--- a/pandas/_libs/index.pyx
+++ b/pandas/_libs/index.pyx
@@ -622,7 +622,7 @@ cdef class BaseMultiIndexCodesEngine:
                        in zip(self.levels, zt)]
         return self._codes_to_ints(np.array(level_codes, dtype='uint64').T)
 
-    def get_indexer(self, target) -> np.ndarray:
+    def get_indexer(self, target: np.ndarray) -> np.ndarray:
         """
         Returns an array giving the positions of each value of `target` in
         `self.values`, where -1 represents a value in `target` which does not
@@ -630,15 +630,14 @@ cdef class BaseMultiIndexCodesEngine:
 
         Parameters
         ----------
-        target : MultiIndex
+        target : np.ndarray
 
         Returns
         -------
         np.ndarray[intp_t, ndim=1] of the indexer of `target` into
         `self.values`
         """
-        lab_ints = self._extract_level_codes(target)
-        return self._base.get_indexer(self, lab_ints)
+        return self._base.get_indexer(self, target)
 
     def get_indexer_with_fill(self, ndarray target, ndarray values,
                               str method, object limit) -> np.ndarray:
@@ -741,10 +740,9 @@ cdef class BaseMultiIndexCodesEngine:
 
         return self._base.get_loc(self, lab_int)
 
-    def get_indexer_non_unique(self, target):
+    def get_indexer_non_unique(self, target: np.ndarray) -> np.ndarray:
         # target: MultiIndex
-        lab_ints = self._extract_level_codes(target)
-        indexer = self._base.get_indexer_non_unique(self, lab_ints)
+        indexer = self._base.get_indexer_non_unique(self, target)
 
         return indexer
 
diff --git a/pandas/core/indexes/base.py b/pandas/core/indexes/base.py
index 12ac954f271d3..87e19ce6ef670 100644
--- a/pandas/core/indexes/base.py
+++ b/pandas/core/indexes/base.py
@@ -3620,9 +3620,8 @@ def _get_indexer(
         else:
             tgt_values = target._get_engine_target()
             if target._is_multi and self._is_multi:
-                # error: Incompatible types in assignment (expression has type
-                # "Index", variable has type "ndarray[Any, Any]")
-                tgt_values = target  # type: ignore[assignment]
+                tgt_values = self._engine._extract_level_codes(target)
+
             indexer = self._engine.get_indexer(tgt_values)
 
         return ensure_platform_int(indexer)
@@ -5465,7 +5464,7 @@ def get_indexer_non_unique(
         #  self and non-Multi target
         tgt_values = target._get_engine_target()
         if self._is_multi and target._is_multi:
-            tgt_values = target
+            tgt_values = self._engine._extract_level_codes(target)
 
         indexer, missing = self._engine.get_indexer_non_unique(tgt_values)
         return ensure_platform_int(indexer), ensure_platform_int(missing)