diff --git a/doc/source/whatsnew/v2.1.0.rst b/doc/source/whatsnew/v2.1.0.rst
index fc09f3d5853a2..23e06b8f0af6e 100644
--- a/doc/source/whatsnew/v2.1.0.rst
+++ b/doc/source/whatsnew/v2.1.0.rst
@@ -28,6 +28,7 @@ enhancement2
 
 Other enhancements
 ^^^^^^^^^^^^^^^^^^
+- :meth:`MultiIndex.sort_values` now supports ``na_position`` (:issue:`51612`)
 - :meth:`MultiIndex.sortlevel` and :meth:`Index.sortlevel` gained a new keyword ``na_position`` (:issue:`51612`)
 - Improve error message when setting :class:`DataFrame` with wrong number of columns through :meth:`DataFrame.isetitem` (:issue:`51701`)
 - Let :meth:`DataFrame.to_feather` accept a non-default :class:`Index` and non-string column names (:issue:`51787`)
diff --git a/pandas/core/indexes/base.py b/pandas/core/indexes/base.py
index 4f89686e5a820..38028eafb0925 100644
--- a/pandas/core/indexes/base.py
+++ b/pandas/core/indexes/base.py
@@ -5597,7 +5597,7 @@ def sort_values(
                 items=idx, ascending=ascending, na_position=na_position, key=key
             )
         else:
-            _as = idx.argsort()
+            _as = idx.argsort(na_position=na_position)
             if not ascending:
                 _as = _as[::-1]
 
diff --git a/pandas/core/indexes/multi.py b/pandas/core/indexes/multi.py
index 857d1fb3f6554..58a5dcb627266 100644
--- a/pandas/core/indexes/multi.py
+++ b/pandas/core/indexes/multi.py
@@ -2132,11 +2132,15 @@ def append(self, other):
         except (TypeError, IndexError):
             return Index(new_tuples)
 
-    def argsort(self, *args, **kwargs) -> npt.NDArray[np.intp]:
+    def argsort(
+        self, *args, na_position: str = "last", **kwargs
+    ) -> npt.NDArray[np.intp]:
         if len(args) == 0 and len(kwargs) == 0:
             # lexsort is significantly faster than self._values.argsort()
             target = self._sort_levels_monotonic(raise_if_incomparable=True)
-            return lexsort_indexer(target._get_codes_for_sorting())
+            return lexsort_indexer(
+                target._get_codes_for_sorting(), na_position=na_position
+            )
         return self._values.argsort(*args, **kwargs)
 
     @Appender(_index_shared_docs["repeat"] % _index_doc_kwargs)
diff --git a/pandas/tests/indexes/multi/test_sorting.py b/pandas/tests/indexes/multi/test_sorting.py
index 9392ff9368c6a..3f1aaebc0f47c 100644
--- a/pandas/tests/indexes/multi/test_sorting.py
+++ b/pandas/tests/indexes/multi/test_sorting.py
@@ -14,6 +14,7 @@
     Index,
     MultiIndex,
     RangeIndex,
+    Series,
     Timestamp,
 )
 import pandas._testing as tm
@@ -311,3 +312,27 @@ def test_sort_values_incomparable():
     match = "'<' not supported between instances of 'Timestamp' and 'int'"
     with pytest.raises(TypeError, match=match):
         mi.sort_values()
+
+
+@pytest.mark.parametrize("na_position", ["first", "last"])
+@pytest.mark.parametrize("dtype", ["float64", "Int64", "Float64"])
+def test_sort_values_with_na_na_position(dtype, na_position):
+    # 51612
+    arrays = [
+        Series([1, 1, 2], dtype=dtype),
+        Series([1, None, 3], dtype=dtype),
+    ]
+    index = MultiIndex.from_arrays(arrays)
+    result = index.sort_values(na_position=na_position)
+    if na_position == "first":
+        arrays = [
+            Series([1, 1, 2], dtype=dtype),
+            Series([None, 1, 3], dtype=dtype),
+        ]
+    else:
+        arrays = [
+            Series([1, 1, 2], dtype=dtype),
+            Series([1, None, 3], dtype=dtype),
+        ]
+    expected = MultiIndex.from_arrays(arrays)
+    tm.assert_index_equal(result, expected)