diff --git a/pandas/compat/__init__.py b/pandas/compat/__init__.py
index 9b6b1ab3b8909..ff99d6b759d66 100644
--- a/pandas/compat/__init__.py
+++ b/pandas/compat/__init__.py
@@ -35,6 +35,7 @@
     pa_version_under17p0,
     pa_version_under18p0,
     pa_version_under19p0,
+    pa_version_under20p0,
 )
 
 if TYPE_CHECKING:
@@ -195,6 +196,7 @@ def get_bz2_file() -> type[pandas.compat.compressors.BZ2File]:
     "pa_version_under17p0",
     "pa_version_under18p0",
     "pa_version_under19p0",
+    "pa_version_under20p0",
     "HAS_PYARROW",
     "IS64",
     "ISMUSL",
diff --git a/pandas/tests/extension/test_arrow.py b/pandas/tests/extension/test_arrow.py
index a63cde8022e24..17fe36c4b4469 100644
--- a/pandas/tests/extension/test_arrow.py
+++ b/pandas/tests/extension/test_arrow.py
@@ -40,6 +40,7 @@
     pa_version_under11p0,
     pa_version_under13p0,
     pa_version_under14p0,
+    pa_version_under20p0,
 )
 
 from pandas.core.dtypes.dtypes import (
@@ -448,6 +449,9 @@ def test_accumulate_series(self, data, all_numeric_accumulations, skipna, reques
         self.check_accumulate(ser, op_name, skipna)
 
     def _supports_reduction(self, ser: pd.Series, op_name: str) -> bool:
+        if op_name == "kurt" or (pa_version_under20p0 and op_name == "skew"):
+            return False
+
         dtype = ser.dtype
         # error: Item "dtype[Any]" of "dtype[Any] | ExtensionDtype" has
         # no attribute "pyarrow_dtype"
@@ -464,7 +468,7 @@ def _supports_reduction(self, ser: pd.Series, op_name: str) -> bool:
                 pass
             else:
                 return False
-        elif pa.types.is_binary(pa_dtype) and op_name == "sum":
+        elif pa.types.is_binary(pa_dtype) and op_name in ["sum", "skew"]:
             return False
         elif (
             pa.types.is_string(pa_dtype) or pa.types.is_binary(pa_dtype)
@@ -525,18 +529,31 @@ def test_reduce_series_numeric(self, data, all_numeric_reductions, skipna, reque
                 f"pyarrow={pa.__version__} for {pa_dtype}"
             ),
         )
-        if all_numeric_reductions in {"skew", "kurt"} and (
-            dtype._is_numeric or dtype.kind == "b"
-        ):
-            request.applymarker(xfail_mark)
-
-        elif pa.types.is_boolean(pa_dtype) and all_numeric_reductions in {
+        if pa.types.is_boolean(pa_dtype) and all_numeric_reductions in {
             "sem",
             "std",
             "var",
             "median",
         }:
             request.applymarker(xfail_mark)
+        elif (
+            not pa_version_under20p0
+            and all_numeric_reductions == "skew"
+            and (
+                pa.types.is_boolean(pa_dtype)
+                or (
+                    skipna
+                    and (
+                        pa.types.is_integer(pa_dtype) or pa.types.is_floating(pa_dtype)
+                    )
+                )
+            )
+        ):
+            request.applymarker(
+                pytest.mark.xfail(
+                    reason="https://github.com/apache/arrow/issues/45733",
+                )
+            )
         super().test_reduce_series_numeric(data, all_numeric_reductions, skipna)
 
     @pytest.mark.parametrize("skipna", [True, False])
@@ -563,7 +580,7 @@ def _get_expected_reduction_dtype(self, arr, op_name: str, skipna: bool):
         if op_name in ["max", "min"]:
             cmp_dtype = arr.dtype
         elif arr.dtype.name == "decimal128(7, 3)[pyarrow]":
-            if op_name not in ["median", "var", "std"]:
+            if op_name not in ["median", "var", "std", "skew"]:
                 cmp_dtype = arr.dtype
             else:
                 cmp_dtype = "float64[pyarrow]"
@@ -582,7 +599,7 @@ def _get_expected_reduction_dtype(self, arr, op_name: str, skipna: bool):
     @pytest.mark.parametrize("skipna", [True, False])
     def test_reduce_frame(self, data, all_numeric_reductions, skipna, request):
         op_name = all_numeric_reductions
-        if op_name == "skew":
+        if op_name == "skew" and pa_version_under20p0:
             if data.dtype._is_numeric:
                 mark = pytest.mark.xfail(reason="skew not implemented")
                 request.applymarker(mark)