diff --git a/pandas/compat/pyarrow.py b/pandas/compat/pyarrow.py
index 9bf7139769baa..f9b9409317774 100644
--- a/pandas/compat/pyarrow.py
+++ b/pandas/compat/pyarrow.py
@@ -12,9 +12,11 @@
     pa_version_under3p0 = _palv < Version("3.0.0")
     pa_version_under4p0 = _palv < Version("4.0.0")
     pa_version_under5p0 = _palv < Version("5.0.0")
+    pa_version_under6p0 = _palv < Version("6.0.0")
 except ImportError:
     pa_version_under1p0 = True
     pa_version_under2p0 = True
     pa_version_under3p0 = True
     pa_version_under4p0 = True
     pa_version_under5p0 = True
+    pa_version_under6p0 = True
diff --git a/pandas/tests/io/parser/test_parse_dates.py b/pandas/tests/io/parser/test_parse_dates.py
index 17c107814995c..c8bea9592e82a 100644
--- a/pandas/tests/io/parser/test_parse_dates.py
+++ b/pandas/tests/io/parser/test_parse_dates.py
@@ -26,6 +26,7 @@
     is_platform_windows,
     np_array_datetime64_compat,
 )
+from pandas.compat.pyarrow import pa_version_under6p0
 
 import pandas as pd
 from pandas import (
@@ -431,6 +432,11 @@ def test_date_col_as_index_col(all_parsers):
         columns=["X0", "X2", "X3", "X4", "X5", "X6", "X7"],
         index=index,
     )
+    if parser.engine == "pyarrow" and not pa_version_under6p0:
+        # https://github.com/pandas-dev/pandas/issues/44231
+        # pyarrow 6.0 starts to infer time type
+        expected["X2"] = pd.to_datetime("1970-01-01" + expected["X2"]).dt.time
+
     tm.assert_frame_equal(result, expected)