diff --git a/doc/source/whatsnew/v2.1.4.rst b/doc/source/whatsnew/v2.1.4.rst
index d61714d9473c6..39cd6b39309cf 100644
--- a/doc/source/whatsnew/v2.1.4.rst
+++ b/doc/source/whatsnew/v2.1.4.rst
@@ -22,6 +22,8 @@ Fixed regressions
 Bug fixes
 ~~~~~~~~~
 - Bug in :meth:`DataFrame.apply` where passing ``raw=True`` ignored ``args`` passed to the applied function (:issue:`55753`)
+- Fixed bug in :meth:`DataFrame.__setitem__` casting :class:`Index` with object-dtype to PyArrow backed strings when ``infer_string`` option is set (:issue:`55638`)
+- Fixed bug in :meth:`Index.insert` casting object-dtype to PyArrow backed strings when ``infer_string`` option is set (:issue:`55638`)
 -
 
 .. ---------------------------------------------------------------------------
diff --git a/pandas/core/construction.py b/pandas/core/construction.py
index 5903187769f08..39f0ddf172e33 100644
--- a/pandas/core/construction.py
+++ b/pandas/core/construction.py
@@ -49,6 +49,7 @@
 from pandas.core.dtypes.common import (
     is_list_like,
     is_object_dtype,
+    is_string_dtype,
     pandas_dtype,
 )
 from pandas.core.dtypes.dtypes import NumpyEADtype
@@ -548,6 +549,10 @@ def sanitize_array(
         # Avoid ending up with a NumpyExtensionArray
         dtype = dtype.numpy_dtype
 
+    object_index = False
+    if isinstance(data, ABCIndex) and data.dtype == object and dtype is None:
+        object_index = True
+
     # extract ndarray or ExtensionArray, ensure we have no NumpyExtensionArray
     data = extract_array(data, extract_numpy=True, extract_range=True)
 
@@ -601,6 +606,13 @@ def sanitize_array(
             subarr = data
             if data.dtype == object:
                 subarr = maybe_infer_to_datetimelike(data)
+                if (
+                    object_index
+                    and using_pyarrow_string_dtype()
+                    and is_string_dtype(subarr)
+                ):
+                    # Avoid inference when string option is set
+                    subarr = data
             elif data.dtype.kind == "U" and using_pyarrow_string_dtype():
                 from pandas.core.arrays.string_ import StringDtype
 
diff --git a/pandas/core/indexes/base.py b/pandas/core/indexes/base.py
index 85b68c1bc2ec7..aaea5a58723a1 100644
--- a/pandas/core/indexes/base.py
+++ b/pandas/core/indexes/base.py
@@ -23,6 +23,7 @@
 from pandas._config import (
     get_option,
     using_copy_on_write,
+    using_pyarrow_string_dtype,
 )
 
 from pandas._libs import (
@@ -6948,7 +6949,14 @@ def insert(self, loc: int, item) -> Index:
             loc = loc if loc >= 0 else loc - 1
             new_values[loc] = item
 
-        return Index._with_infer(new_values, name=self.name)
+        idx = Index._with_infer(new_values, name=self.name)
+        if (
+            using_pyarrow_string_dtype()
+            and is_string_dtype(idx.dtype)
+            and new_values.dtype == object
+        ):
+            idx = idx.astype(new_values.dtype)
+        return idx
 
     def drop(
         self,
diff --git a/pandas/tests/frame/indexing/test_indexing.py b/pandas/tests/frame/indexing/test_indexing.py
index de8df15a9d747..51b0a0a13d90b 100644
--- a/pandas/tests/frame/indexing/test_indexing.py
+++ b/pandas/tests/frame/indexing/test_indexing.py
@@ -1913,7 +1913,7 @@ def test_add_new_column_infer_string():
         df.loc[df["x"] == 1, "y"] = "1"
     expected = DataFrame(
         {"x": [1], "y": Series(["1"], dtype="string[pyarrow_numpy]")},
-        columns=Index(["x", "y"], dtype="string[pyarrow_numpy]"),
+        columns=Index(["x", "y"], dtype=object),
     )
     tm.assert_frame_equal(df, expected)
 
diff --git a/pandas/tests/frame/indexing/test_setitem.py b/pandas/tests/frame/indexing/test_setitem.py
index ccc1249088f9a..fc2e817b1600e 100644
--- a/pandas/tests/frame/indexing/test_setitem.py
+++ b/pandas/tests/frame/indexing/test_setitem.py
@@ -753,6 +753,15 @@ def test_setitem_frame_overwrite_with_ea_dtype(self, any_numeric_ea_dtype):
         )
         tm.assert_frame_equal(df, expected)
 
+    def test_setitem_string_option_object_index(self):
+        # GH#55638
+        pytest.importorskip("pyarrow")
+        df = DataFrame({"a": [1, 2]})
+        with pd.option_context("future.infer_string", True):
+            df["b"] = Index(["a", "b"], dtype=object)
+        expected = DataFrame({"a": [1, 2], "b": Series(["a", "b"], dtype=object)})
+        tm.assert_frame_equal(df, expected)
+
     def test_setitem_frame_midx_columns(self):
         # GH#49121
         df = DataFrame({("a", "b"): [10]})