diff --git a/doc/source/whatsnew/v1.3.0.rst b/doc/source/whatsnew/v1.3.0.rst
index ac5ad12a992b7..42396d920c3bd 100644
--- a/doc/source/whatsnew/v1.3.0.rst
+++ b/doc/source/whatsnew/v1.3.0.rst
@@ -437,6 +437,7 @@ Timezones
 Numeric
 ^^^^^^^
 - Bug in :meth:`DataFrame.quantile`, :meth:`DataFrame.sort_values` causing incorrect subsequent indexing behavior (:issue:`38351`)
+- Bug in :meth:`DataFrame.sort_values` raising an :class:`IndexError` for empty ``by`` (:issue:`40258`)
 - Bug in :meth:`DataFrame.select_dtypes` with ``include=np.number`` now retains numeric ``ExtensionDtype`` columns (:issue:`35340`)
 - Bug in :meth:`DataFrame.mode` and :meth:`Series.mode` not keeping consistent integer :class:`Index` for empty input (:issue:`33321`)
 - Bug in :meth:`DataFrame.rank` with ``np.inf`` and mixture of ``np.nan`` and ``np.inf`` (:issue:`32593`)
diff --git a/pandas/core/frame.py b/pandas/core/frame.py
index dbf2446f43af3..64759dcf07d8b 100644
--- a/pandas/core/frame.py
+++ b/pandas/core/frame.py
@@ -5818,7 +5818,7 @@ def sort_values(  # type: ignore[override]
                 keys, orders=ascending, na_position=na_position, key=key
             )
             indexer = ensure_platform_int(indexer)
-        else:
+        elif len(by):
 
             by = by[0]
             k = self._get_label_or_level_values(by, axis=axis)
@@ -5833,6 +5833,8 @@ def sort_values(  # type: ignore[override]
             indexer = nargsort(
                 k, kind=kind, ascending=ascending, na_position=na_position, key=key
             )
+        else:
+            return self.copy()
 
         new_data = self._mgr.take(
             indexer, axis=self._get_block_manager_axis(axis), verify=False
diff --git a/pandas/tests/frame/methods/test_sort_values.py b/pandas/tests/frame/methods/test_sort_values.py
index eaea22df3adfe..2ca5f6aa72241 100644
--- a/pandas/tests/frame/methods/test_sort_values.py
+++ b/pandas/tests/frame/methods/test_sort_values.py
@@ -79,6 +79,13 @@ def test_sort_values(self):
         with pytest.raises(ValueError, match=msg):
             frame.sort_values(by=["A", "B"], axis=0, ascending=[True] * 5)
 
+    def test_sort_values_by_empty_list(self):
+        # https://github.com/pandas-dev/pandas/issues/40258
+        expected = DataFrame({"a": [1, 4, 2, 5, 3, 6]})
+        result = expected.sort_values(by=[])
+        tm.assert_frame_equal(result, expected)
+        assert result is not expected
+
     def test_sort_values_inplace(self):
         frame = DataFrame(
             np.random.randn(4, 4), index=[1, 2, 3, 4], columns=["A", "B", "C", "D"]