diff --git a/doc/source/whatsnew/v1.5.0.rst b/doc/source/whatsnew/v1.5.0.rst
index 02db4cbe0e8a5..1913e3857f2d3 100644
--- a/doc/source/whatsnew/v1.5.0.rst
+++ b/doc/source/whatsnew/v1.5.0.rst
@@ -294,6 +294,7 @@ 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`)
 - :class:`Interval` now supports checking whether one interval is contained by another interval (:issue:`46613`)
+- Added ``copy`` keyword to :meth:`Series.set_axis` and :meth:`DataFrame.set_axis` to allow user to set axis on a new object without necessarily copying the underlying data (:issue:`47932`)
 - :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`)
 
diff --git a/pandas/core/frame.py b/pandas/core/frame.py
index 6cfca4ebdc612..9adcfddc4006c 100644
--- a/pandas/core/frame.py
+++ b/pandas/core/frame.py
@@ -5036,17 +5036,34 @@ def align(
 
     @overload
     def set_axis(
-        self, labels, *, axis: Axis = ..., inplace: Literal[False] = ...
+        self,
+        labels,
+        *,
+        axis: Axis = ...,
+        inplace: Literal[False] = ...,
+        copy: bool | lib.NoDefault = ...,
     ) -> DataFrame:
         ...
 
     @overload
-    def set_axis(self, labels, *, axis: Axis = ..., inplace: Literal[True]) -> None:
+    def set_axis(
+        self,
+        labels,
+        *,
+        axis: Axis = ...,
+        inplace: Literal[True],
+        copy: bool | lib.NoDefault = ...,
+    ) -> None:
         ...
 
     @overload
     def set_axis(
-        self, labels, *, axis: Axis = ..., inplace: bool = ...
+        self,
+        labels,
+        *,
+        axis: Axis = ...,
+        inplace: bool = ...,
+        copy: bool | lib.NoDefault = ...,
     ) -> DataFrame | None:
         ...
 
@@ -5091,10 +5108,15 @@ def set_axis(
         see_also_sub=" or columns",
     )
     @Appender(NDFrame.set_axis.__doc__)
-    def set_axis(  # type: ignore[override]
-        self, labels, axis: Axis = 0, inplace: bool = False
-    ) -> DataFrame | None:
-        return super().set_axis(labels, axis=axis, inplace=inplace)
+    def set_axis(
+        self,
+        labels,
+        axis: Axis = 0,
+        inplace: bool = False,
+        *,
+        copy: bool | lib.NoDefault = lib.no_default,
+    ):
+        return super().set_axis(labels, axis=axis, inplace=inplace, copy=copy)
 
     @Substitution(**_shared_doc_kwargs)
     @Appender(NDFrame.reindex.__doc__)
diff --git a/pandas/core/generic.py b/pandas/core/generic.py
index d9264e8a18f2e..7de75be78e6dd 100644
--- a/pandas/core/generic.py
+++ b/pandas/core/generic.py
@@ -711,23 +711,45 @@ def size(self) -> int:
 
     @overload
     def set_axis(
-        self: NDFrameT, labels, *, axis: Axis = ..., inplace: Literal[False] = ...
+        self: NDFrameT,
+        labels,
+        *,
+        axis: Axis = ...,
+        inplace: Literal[False] = ...,
+        copy: bool_t | lib.NoDefault = ...,
     ) -> NDFrameT:
         ...
 
     @overload
-    def set_axis(self, labels, *, axis: Axis = ..., inplace: Literal[True]) -> None:
+    def set_axis(
+        self,
+        labels,
+        *,
+        axis: Axis = ...,
+        inplace: Literal[True],
+        copy: bool_t | lib.NoDefault = ...,
+    ) -> None:
         ...
 
     @overload
     def set_axis(
-        self: NDFrameT, labels, *, axis: Axis = ..., inplace: bool_t = ...
+        self: NDFrameT,
+        labels,
+        *,
+        axis: Axis = ...,
+        inplace: bool_t = ...,
+        copy: bool_t | lib.NoDefault = ...,
     ) -> NDFrameT | None:
         ...
 
     @deprecate_nonkeyword_arguments(version=None, allowed_args=["self", "labels"])
     def set_axis(
-        self: NDFrameT, labels, axis: Axis = 0, inplace: bool_t = False
+        self: NDFrameT,
+        labels,
+        axis: Axis = 0,
+        inplace: bool_t = False,
+        *,
+        copy: bool_t | lib.NoDefault = lib.no_default,
     ) -> NDFrameT | None:
         """
         Assign desired index to given axis.
@@ -747,6 +769,11 @@ def set_axis(
         inplace : bool, default False
             Whether to return a new %(klass)s instance.
 
+        copy : bool, default True
+            Whether to make a copy of the underlying data.
+
+            .. versionadded:: 1.5.0
+
         Returns
         -------
         renamed : %(klass)s or None
@@ -756,16 +783,25 @@ def set_axis(
         --------
         %(klass)s.rename_axis : Alter the name of the index%(see_also_sub)s.
         """
+        if inplace:
+            if copy is True:
+                raise ValueError("Cannot specify both inplace=True and copy=True")
+            copy = False
+        elif copy is lib.no_default:
+            copy = True
+
         self._check_inplace_and_allows_duplicate_labels(inplace)
-        return self._set_axis_nocheck(labels, axis, inplace)
+        return self._set_axis_nocheck(labels, axis, inplace, copy=copy)
 
     @final
-    def _set_axis_nocheck(self, labels, axis: Axis, inplace: bool_t):
+    def _set_axis_nocheck(self, labels, axis: Axis, inplace: bool_t, copy: bool_t):
         # NDFrame.rename with inplace=False calls set_axis(inplace=True) on a copy.
         if inplace:
             setattr(self, self._get_axis_name(axis), labels)
         else:
-            obj = self.copy()
+            # With copy=False, we create a new object but don't copy the
+            #  underlying data.
+            obj = self.copy(deep=copy)
             obj.set_axis(labels, axis=axis, inplace=True)
             return obj
 
@@ -1053,7 +1089,7 @@ def _rename(
                     raise KeyError(f"{missing_labels} not found in axis")
 
             new_index = ax._transform_index(f, level=level)
-            result._set_axis_nocheck(new_index, axis=axis_no, inplace=True)
+            result._set_axis_nocheck(new_index, axis=axis_no, inplace=True, copy=False)
             result._clear_item_cache()
 
         if inplace:
diff --git a/pandas/core/series.py b/pandas/core/series.py
index b1ad3ab175d1b..f55d6a26255a0 100644
--- a/pandas/core/series.py
+++ b/pandas/core/series.py
@@ -4976,17 +4976,34 @@ def rename(
 
     @overload
     def set_axis(
-        self, labels, *, axis: Axis = ..., inplace: Literal[False] = ...
+        self,
+        labels,
+        *,
+        axis: Axis = ...,
+        inplace: Literal[False] = ...,
+        copy: bool | lib.NoDefault = ...,
     ) -> Series:
         ...
 
     @overload
-    def set_axis(self, labels, *, axis: Axis = ..., inplace: Literal[True]) -> None:
+    def set_axis(
+        self,
+        labels,
+        *,
+        axis: Axis = ...,
+        inplace: Literal[True],
+        copy: bool | lib.NoDefault = ...,
+    ) -> None:
         ...
 
     @overload
     def set_axis(
-        self, labels, *, axis: Axis = ..., inplace: bool = ...
+        self,
+        labels,
+        *,
+        axis: Axis = ...,
+        inplace: bool = ...,
+        copy: bool | lib.NoDefault = ...,
     ) -> Series | None:
         ...
 
@@ -5018,9 +5035,13 @@ def set_axis(
     )
     @Appender(NDFrame.set_axis.__doc__)
     def set_axis(  # type: ignore[override]
-        self, labels, axis: Axis = 0, inplace: bool = False
+        self,
+        labels,
+        axis: Axis = 0,
+        inplace: bool = False,
+        copy: bool | lib.NoDefault = lib.no_default,
     ) -> Series | None:
-        return super().set_axis(labels, axis=axis, inplace=inplace)
+        return super().set_axis(labels, axis=axis, inplace=inplace, copy=copy)
 
     # error: Cannot determine type of 'reindex'
     @doc(
diff --git a/pandas/tests/frame/methods/test_set_axis.py b/pandas/tests/frame/methods/test_set_axis.py
index 3284243ddac48..67488dff3c335 100644
--- a/pandas/tests/frame/methods/test_set_axis.py
+++ b/pandas/tests/frame/methods/test_set_axis.py
@@ -24,6 +24,69 @@ def test_set_axis(self, obj):
         result = obj.set_axis(new_index, axis=0, inplace=False)
         tm.assert_equal(expected, result)
 
+    def test_set_axis_copy(self, obj):
+        # Test copy keyword GH#47932
+        new_index = list("abcd")[: len(obj)]
+
+        orig = obj.iloc[:]
+        expected = obj.copy()
+        expected.index = new_index
+
+        with pytest.raises(
+            ValueError, match="Cannot specify both inplace=True and copy=True"
+        ):
+            obj.set_axis(new_index, axis=0, inplace=True, copy=True)
+
+        result = obj.set_axis(new_index, axis=0, copy=True)
+        tm.assert_equal(expected, result)
+        assert result is not obj
+        # check we DID make a copy
+        if obj.ndim == 1:
+            assert not tm.shares_memory(result, obj)
+        else:
+            assert not any(
+                tm.shares_memory(result.iloc[:, i], obj.iloc[:, i])
+                for i in range(obj.shape[1])
+            )
+
+        result = obj.set_axis(new_index, axis=0, copy=False)
+        tm.assert_equal(expected, result)
+        assert result is not obj
+        # check we did NOT make a copy
+        if obj.ndim == 1:
+            assert tm.shares_memory(result, obj)
+        else:
+            assert all(
+                tm.shares_memory(result.iloc[:, i], obj.iloc[:, i])
+                for i in range(obj.shape[1])
+            )
+
+        # copy defaults to True
+        result = obj.set_axis(new_index, axis=0)
+        tm.assert_equal(expected, result)
+        assert result is not obj
+        # check we DID make a copy
+        if obj.ndim == 1:
+            assert not tm.shares_memory(result, obj)
+        else:
+            assert not any(
+                tm.shares_memory(result.iloc[:, i], obj.iloc[:, i])
+                for i in range(obj.shape[1])
+            )
+
+        # Do this last since it alters obj inplace
+        res = obj.set_axis(new_index, inplace=True, copy=False)
+        assert res is None
+        tm.assert_equal(expected, obj)
+        # check we did NOT make a copy
+        if obj.ndim == 1:
+            assert tm.shares_memory(obj, orig)
+        else:
+            assert all(
+                tm.shares_memory(obj.iloc[:, i], orig.iloc[:, i])
+                for i in range(obj.shape[1])
+            )
+
     @pytest.mark.parametrize("axis", [0, "index", 1, "columns"])
     def test_set_axis_inplace_axis(self, axis, obj):
         # GH#14636