diff --git a/doc/source/whatsnew/v1.2.0.rst b/doc/source/whatsnew/v1.2.0.rst
index f751a91cecf19..fba430ac1b5b6 100644
--- a/doc/source/whatsnew/v1.2.0.rst
+++ b/doc/source/whatsnew/v1.2.0.rst
@@ -553,6 +553,7 @@ Reshaping
 - Bug in :meth:`DataFrame.agg` with ``func={'name':<FUNC>}`` incorrectly raising ``TypeError`` when ``DataFrame.columns==['Name']`` (:issue:`36212`)
 - Bug in :meth:`Series.transform` would give incorrect results or raise when the argument ``func`` was dictionary (:issue:`35811`)
 - Bug in :meth:`DataFrame.pivot` did not preserve :class:`MultiIndex` level names for columns when rows and columns both multiindexed (:issue:`36360`)
+- Bug in :meth:`DataFrame.pivot` modified ``index`` argument when ``columns`` was passed but ``values`` was not (:issue:`37635`)
 - Bug in :func:`join` returned a non deterministic level-order for the resulting :class:`MultiIndex` (:issue:`36910`)
 - Bug in :meth:`DataFrame.combine_first()` caused wrong alignment with dtype ``string`` and one level of ``MultiIndex`` containing only ``NA`` (:issue:`37591`)
 - Fixed regression in :func:`merge` on merging DatetimeIndex with empty DataFrame (:issue:`36895`)
diff --git a/pandas/core/reshape/pivot.py b/pandas/core/reshape/pivot.py
index 8fae01cb30d3d..c1198cdfcda81 100644
--- a/pandas/core/reshape/pivot.py
+++ b/pandas/core/reshape/pivot.py
@@ -450,10 +450,9 @@ def pivot(
             cols = com.convert_to_list_like(index)
         else:
             cols = []
-        cols.extend(columns)
 
         append = index is None
-        indexed = data.set_index(cols, append=append)
+        indexed = data.set_index(cols + columns, append=append)
     else:
         if index is None:
             index = [Series(data.index, name=data.index.name)]
diff --git a/pandas/tests/reshape/test_pivot.py b/pandas/tests/reshape/test_pivot.py
index adab64577ee7a..e08876226cbc8 100644
--- a/pandas/tests/reshape/test_pivot.py
+++ b/pandas/tests/reshape/test_pivot.py
@@ -2153,3 +2153,41 @@ def test_pivot_index_none(self):
 
         expected.columns.name = "columns"
         tm.assert_frame_equal(result, expected)
+
+    def test_pivot_index_list_values_none_immutable_args(self):
+        # GH37635
+        df = DataFrame(
+            {
+                "lev1": [1, 1, 1, 2, 2, 2],
+                "lev2": [1, 1, 2, 1, 1, 2],
+                "lev3": [1, 2, 1, 2, 1, 2],
+                "lev4": [1, 2, 3, 4, 5, 6],
+                "values": [0, 1, 2, 3, 4, 5],
+            }
+        )
+        index = ["lev1", "lev2"]
+        columns = ["lev3"]
+        result = df.pivot(index=index, columns=columns, values=None)
+
+        expected = DataFrame(
+            np.array(
+                [
+                    [1.0, 2.0, 0.0, 1.0],
+                    [3.0, np.nan, 2.0, np.nan],
+                    [5.0, 4.0, 4.0, 3.0],
+                    [np.nan, 6.0, np.nan, 5.0],
+                ]
+            ),
+            index=MultiIndex.from_arrays(
+                [(1, 1, 2, 2), (1, 2, 1, 2)], names=["lev1", "lev2"]
+            ),
+            columns=MultiIndex.from_arrays(
+                [("lev4", "lev4", "values", "values"), (1, 2, 1, 2)],
+                names=[None, "lev3"],
+            ),
+        )
+
+        tm.assert_frame_equal(result, expected)
+
+        assert index == ["lev1", "lev2"]
+        assert columns == ["lev3"]