diff --git a/doc/source/whatsnew/v3.0.0.rst b/doc/source/whatsnew/v3.0.0.rst
index 64e4a30453366..7cd5759af4989 100644
--- a/doc/source/whatsnew/v3.0.0.rst
+++ b/doc/source/whatsnew/v3.0.0.rst
@@ -670,6 +670,7 @@ Conversion
 - Bug in :meth:`DataFrame.astype` not casting ``values`` for Arrow-based dictionary dtype correctly (:issue:`58479`)
 - Bug in :meth:`DataFrame.update` bool dtype being converted to object (:issue:`55509`)
 - Bug in :meth:`Series.astype` might modify read-only array inplace when casting to a string dtype (:issue:`57212`)
+- Bug in :meth:`Series.convert_dtypes` and :meth:`DataFrame.convert_dtypes` removing timezone information for objects with :class:`ArrowDtype` (:issue:`60237`)
 - Bug in :meth:`Series.reindex` not maintaining ``float32`` type when a ``reindex`` introduces a missing value (:issue:`45857`)
 
 Strings
diff --git a/pandas/core/dtypes/cast.py b/pandas/core/dtypes/cast.py
index 94531c2ac87e8..f11aefeeaaa00 100644
--- a/pandas/core/dtypes/cast.py
+++ b/pandas/core/dtypes/cast.py
@@ -1113,7 +1113,7 @@ def convert_dtypes(
     else:
         inferred_dtype = input_array.dtype
 
-    if dtype_backend == "pyarrow":
+    if dtype_backend == "pyarrow" and not isinstance(inferred_dtype, ArrowDtype):
         from pandas.core.arrays.arrow.array import to_pyarrow_type
         from pandas.core.arrays.string_ import StringDtype
 
diff --git a/pandas/tests/frame/methods/test_convert_dtypes.py b/pandas/tests/frame/methods/test_convert_dtypes.py
index e7f6e5d625d3e..d0f30204758d3 100644
--- a/pandas/tests/frame/methods/test_convert_dtypes.py
+++ b/pandas/tests/frame/methods/test_convert_dtypes.py
@@ -196,3 +196,18 @@ def test_convert_dtypes_from_arrow(self):
         result = df.convert_dtypes()
         expected = df.astype({"a": "string[python]"})
         tm.assert_frame_equal(result, expected)
+
+    def test_convert_dtype_pyarrow_timezone_preserve(self):
+        # GH 60237
+        pytest.importorskip("pyarrow")
+        df = pd.DataFrame(
+            {
+                "timestamps": pd.Series(
+                    pd.to_datetime(range(5), utc=True, unit="h"),
+                    dtype="timestamp[ns, tz=UTC][pyarrow]",
+                )
+            }
+        )
+        result = df.convert_dtypes(dtype_backend="pyarrow")
+        expected = df.copy()
+        tm.assert_frame_equal(result, expected)
diff --git a/pandas/tests/series/methods/test_convert_dtypes.py b/pandas/tests/series/methods/test_convert_dtypes.py
index 90c4056a39e84..d373386108ff6 100644
--- a/pandas/tests/series/methods/test_convert_dtypes.py
+++ b/pandas/tests/series/methods/test_convert_dtypes.py
@@ -297,3 +297,14 @@ def test_convert_dtypes_pyarrow_null(self):
         result = ser.convert_dtypes(dtype_backend="pyarrow")
         expected = pd.Series([None, None], dtype=pd.ArrowDtype(pa.null()))
         tm.assert_series_equal(result, expected)
+
+    def test_convert_dtype_pyarrow_timezone_preserve(self):
+        # GH 60237
+        pytest.importorskip("pyarrow")
+        ser = pd.Series(
+            pd.to_datetime(range(5), utc=True, unit="h"),
+            dtype="timestamp[ns, tz=UTC][pyarrow]",
+        )
+        result = ser.convert_dtypes(dtype_backend="pyarrow")
+        expected = ser.copy()
+        tm.assert_series_equal(result, expected)