diff --git a/doc/source/whatsnew/v1.5.0.rst b/doc/source/whatsnew/v1.5.0.rst
index a0d33cb513722..f51f31af4799a 100644
--- a/doc/source/whatsnew/v1.5.0.rst
+++ b/doc/source/whatsnew/v1.5.0.rst
@@ -843,6 +843,7 @@ Other Deprecations
 - Deprecated setting a categorical's categories with ``cat.categories = ['a', 'b', 'c']``, use :meth:`Categorical.rename_categories` instead (:issue:`37643`)
 - Deprecated unused arguments ``encoding`` and ``verbose`` in :meth:`Series.to_excel` and :meth:`DataFrame.to_excel` (:issue:`47912`)
 - Deprecated producing a single element when iterating over a :class:`DataFrameGroupBy` or a :class:`SeriesGroupBy` that has been grouped by a list of length 1; A tuple of length one will be returned instead (:issue:`42795`)
+- Fixed up warning message of deprecation of :meth:`MultiIndex.lesort_depth` as public method, as the message previously referred to :meth:`MultiIndex.is_lexsorted` instead (:issue:`38701`)
 
 .. ---------------------------------------------------------------------------
 .. _whatsnew_150.performance:
diff --git a/pandas/core/indexes/multi.py b/pandas/core/indexes/multi.py
index 5a9b1e6943608..493d03ed1a86c 100644
--- a/pandas/core/indexes/multi.py
+++ b/pandas/core/indexes/multi.py
@@ -1910,7 +1910,7 @@ def _is_lexsorted(self) -> bool:
     @property
     def lexsort_depth(self) -> int:
         warnings.warn(
-            "MultiIndex.is_lexsorted is deprecated as a public function, "
+            "MultiIndex.lexsort_depth is deprecated as a public function, "
             "users should use MultiIndex.is_monotonic_increasing instead.",
             FutureWarning,
             stacklevel=find_stack_level(),
diff --git a/pandas/tests/indexes/multi/test_lexsort.py b/pandas/tests/indexes/multi/test_lexsort.py
index c37172ad7a980..0aadbdb5c32da 100644
--- a/pandas/tests/indexes/multi/test_lexsort.py
+++ b/pandas/tests/indexes/multi/test_lexsort.py
@@ -24,7 +24,10 @@ def test_is_lexsorted(self):
 
     def test_is_lexsorted_deprecation(self):
         # GH 32259
-        with tm.assert_produces_warning():
+        with tm.assert_produces_warning(
+            FutureWarning,
+            match="MultiIndex.is_lexsorted is deprecated as a public function",
+        ):
             MultiIndex.from_arrays([["a", "b", "c"], ["d", "f", "e"]]).is_lexsorted()
 
 
@@ -53,5 +56,8 @@ def test_lexsort_depth(self):
 
     def test_lexsort_depth_deprecation(self):
         # GH 32259
-        with tm.assert_produces_warning():
+        with tm.assert_produces_warning(
+            FutureWarning,
+            match="MultiIndex.lexsort_depth is deprecated as a public function",
+        ):
             MultiIndex.from_arrays([["a", "b", "c"], ["d", "f", "e"]]).lexsort_depth