diff --git a/doc/source/whatsnew/v1.5.0.rst b/doc/source/whatsnew/v1.5.0.rst
index 48ca1fd9d16eb..b71d294b97f9a 100644
--- a/doc/source/whatsnew/v1.5.0.rst
+++ b/doc/source/whatsnew/v1.5.0.rst
@@ -293,6 +293,7 @@ Other enhancements
 - :meth:`RangeIndex.union` now can return a :class:`RangeIndex` instead of a :class:`Int64Index` if the resulting values are equally spaced (:issue:`47557`, :issue:`43885`)
 - :meth:`DataFrame.compare` now accepts an argument ``result_names`` to allow the user to specify the result's names of both left and right DataFrame which are being compared. This is by default ``'self'`` and ``'other'`` (:issue:`44354`)
 - :meth:`Series.add_suffix`, :meth:`DataFrame.add_suffix`, :meth:`Series.add_prefix` and :meth:`DataFrame.add_prefix` support a ``copy`` argument. If ``False``, the underlying data is not copied in the returned object (:issue:`47934`)
+- :meth:`DataFrame.set_index` now supports a ``copy`` keyword. If ``False``, the underlying data is not copied when a new :class:`DataFrame` is returned (:issue:`48043`)
 
 .. ---------------------------------------------------------------------------
 .. _whatsnew_150.notable_bug_fixes:
diff --git a/pandas/core/frame.py b/pandas/core/frame.py
index 0a7a6494d04eb..8c4924a2483be 100644
--- a/pandas/core/frame.py
+++ b/pandas/core/frame.py
@@ -5824,6 +5824,7 @@ def set_index(
         append: bool = ...,
         inplace: Literal[False] = ...,
         verify_integrity: bool = ...,
+        copy: bool | lib.NoDefault = ...,
     ) -> DataFrame:
         ...
 
@@ -5836,6 +5837,7 @@ def set_index(
         append: bool = ...,
         inplace: Literal[True],
         verify_integrity: bool = ...,
+        copy: bool | lib.NoDefault = ...,
     ) -> None:
         ...
 
@@ -5847,6 +5849,7 @@ def set_index(
         append: bool = False,
         inplace: bool = False,
         verify_integrity: bool = False,
+        copy: bool | lib.NoDefault = lib.no_default,
     ) -> DataFrame | None:
         """
         Set the DataFrame index using existing columns.
@@ -5873,6 +5876,11 @@ def set_index(
             Check the new index for duplicates. Otherwise defer the check until
             necessary. Setting to False will improve the performance of this
             method.
+        copy : bool, default True
+            Whether to make a copy of the underlying data when returning a new
+            DataFrame.
+
+            .. versionadded:: 1.5.0
 
         Returns
         -------
@@ -5938,6 +5946,13 @@ def set_index(
         4 16     10  2014    31
         """
         inplace = validate_bool_kwarg(inplace, "inplace")
+        if inplace:
+            if copy is not lib.no_default:
+                raise ValueError("Cannot specify copy when inplace=True")
+            copy = False
+        elif copy is lib.no_default:
+            copy = True
+
         self._check_inplace_and_allows_duplicate_labels(inplace)
         if not isinstance(keys, list):
             keys = [keys]
@@ -5973,7 +5988,7 @@ def set_index(
         if inplace:
             frame = self
         else:
-            frame = self.copy()
+            frame = self.copy(deep=copy)
 
         arrays = []
         names: list[Hashable] = []
diff --git a/pandas/tests/frame/methods/test_set_index.py b/pandas/tests/frame/methods/test_set_index.py
index 4c39cf99f18ff..9392d3c146942 100644
--- a/pandas/tests/frame/methods/test_set_index.py
+++ b/pandas/tests/frame/methods/test_set_index.py
@@ -25,6 +25,25 @@
 
 
 class TestSetIndex:
+    def test_set_index_copy(self):
+        # GH#48043
+        df = DataFrame({"A": [1, 2], "B": [3, 4], "C": [5, 6]})
+        expected = DataFrame({"B": [3, 4], "C": [5, 6]}, index=Index([1, 2], name="A"))
+
+        res = df.set_index("A", copy=True)
+        tm.assert_frame_equal(res, expected)
+        assert not any(tm.shares_memory(df[col], res[col]) for col in res.columns)
+
+        res = df.set_index("A", copy=False)
+        tm.assert_frame_equal(res, expected)
+        assert all(tm.shares_memory(df[col], res[col]) for col in res.columns)
+
+        msg = "Cannot specify copy when inplace=True"
+        with pytest.raises(ValueError, match=msg):
+            df.set_index("A", inplace=True, copy=True)
+        with pytest.raises(ValueError, match=msg):
+            df.set_index("A", inplace=True, copy=False)
+
     def test_set_index_multiindex(self):
         # segfault in GH#3308
         d = {"t1": [2, 2.5, 3], "t2": [4, 5, 6]}