diff --git a/doc/source/whatsnew/v2.1.0.rst b/doc/source/whatsnew/v2.1.0.rst
index d1a689dc60830..8a9f786fa87b2 100644
--- a/doc/source/whatsnew/v2.1.0.rst
+++ b/doc/source/whatsnew/v2.1.0.rst
@@ -264,6 +264,7 @@ Other enhancements
 - Many read/to_* functions, such as :meth:`DataFrame.to_pickle` and :func:`read_csv`, support forwarding compression arguments to lzma.LZMAFile (:issue:`52979`)
 - Reductions :meth:`Series.argmax`, :meth:`Series.argmin`, :meth:`Series.idxmax`, :meth:`Series.idxmin`, :meth:`Index.argmax`, :meth:`Index.argmin`, :meth:`DataFrame.idxmax`, :meth:`DataFrame.idxmin` are now supported for object-dtype objects (:issue:`4279`, :issue:`18021`, :issue:`40685`, :issue:`43697`)
 - :meth:`DataFrame.to_parquet` and :func:`read_parquet` will now write and read ``attrs`` respectively (:issue:`54346`)
+- :meth:`Series.cummax`, :meth:`Series.cummin` and :meth:`Series.cumprod` are now supported for pyarrow dtypes with pyarrow version 13.0 and above (:issue:`52085`)
 - Added support for the DataFrame Consortium Standard (:issue:`54383`)
 - Performance improvement in :meth:`.GroupBy.quantile` (:issue:`51722`)
 
diff --git a/pandas/core/arrays/arrow/array.py b/pandas/core/arrays/arrow/array.py
index 0f46e5a4e7482..3c65e6b4879e2 100644
--- a/pandas/core/arrays/arrow/array.py
+++ b/pandas/core/arrays/arrow/array.py
@@ -1389,6 +1389,9 @@ def _accumulate(
         NotImplementedError : subclass does not define accumulations
         """
         pyarrow_name = {
+            "cummax": "cumulative_max",
+            "cummin": "cumulative_min",
+            "cumprod": "cumulative_prod_checked",
             "cumsum": "cumulative_sum_checked",
         }.get(name, name)
         pyarrow_meth = getattr(pc, pyarrow_name, None)
@@ -1398,12 +1401,20 @@ def _accumulate(
         data_to_accum = self._pa_array
 
         pa_dtype = data_to_accum.type
-        if pa.types.is_duration(pa_dtype):
-            data_to_accum = data_to_accum.cast(pa.int64())
+
+        convert_to_int = (
+            pa.types.is_temporal(pa_dtype) and name in ["cummax", "cummin"]
+        ) or (pa.types.is_duration(pa_dtype) and name == "cumsum")
+
+        if convert_to_int:
+            if pa_dtype.bit_width == 32:
+                data_to_accum = data_to_accum.cast(pa.int32())
+            else:
+                data_to_accum = data_to_accum.cast(pa.int64())
 
         result = pyarrow_meth(data_to_accum, skip_nulls=skipna, **kwargs)
 
-        if pa.types.is_duration(pa_dtype):
+        if convert_to_int:
             result = result.cast(pa_dtype)
 
         return type(self)(result)
diff --git a/pandas/tests/extension/test_arrow.py b/pandas/tests/extension/test_arrow.py
index 4c05049ddfcf5..01dedc86c8dca 100644
--- a/pandas/tests/extension/test_arrow.py
+++ b/pandas/tests/extension/test_arrow.py
@@ -339,10 +339,15 @@ def test_from_sequence_of_strings_pa_array(self, data, request):
     def check_accumulate(self, ser, op_name, skipna):
         result = getattr(ser, op_name)(skipna=skipna)
 
-        if ser.dtype.kind == "m":
+        pa_type = ser.dtype.pyarrow_dtype
+        if pa.types.is_temporal(pa_type):
             # Just check that we match the integer behavior.
-            ser = ser.astype("int64[pyarrow]")
-            result = result.astype("int64[pyarrow]")
+            if pa_type.bit_width == 32:
+                int_type = "int32[pyarrow]"
+            else:
+                int_type = "int64[pyarrow]"
+            ser = ser.astype(int_type)
+            result = result.astype(int_type)
 
         result = result.astype("Float64")
         expected = getattr(ser.astype("Float64"), op_name)(skipna=skipna)
@@ -353,14 +358,20 @@ def _supports_accumulation(self, ser: pd.Series, op_name: str) -> bool:
         # attribute "pyarrow_dtype"
         pa_type = ser.dtype.pyarrow_dtype  # type: ignore[union-attr]
 
-        if pa.types.is_string(pa_type) or pa.types.is_binary(pa_type):
-            if op_name in ["cumsum", "cumprod"]:
+        if (
+            pa.types.is_string(pa_type)
+            or pa.types.is_binary(pa_type)
+            or pa.types.is_decimal(pa_type)
+        ):
+            if op_name in ["cumsum", "cumprod", "cummax", "cummin"]:
                 return False
-        elif pa.types.is_temporal(pa_type) and not pa.types.is_duration(pa_type):
-            if op_name in ["cumsum", "cumprod"]:
+        elif pa.types.is_boolean(pa_type):
+            if op_name in ["cumprod", "cummax", "cummin"]:
                 return False
-        elif pa.types.is_duration(pa_type):
-            if op_name == "cumprod":
+        elif pa.types.is_temporal(pa_type):
+            if op_name == "cumsum" and not pa.types.is_duration(pa_type):
+                return False
+            elif op_name == "cumprod":
                 return False
         return True
 
@@ -376,7 +387,9 @@ def test_accumulate_series(self, data, all_numeric_accumulations, skipna, reques
                 data, all_numeric_accumulations, skipna
             )
 
-        if all_numeric_accumulations != "cumsum" or pa_version_under9p0:
+        if pa_version_under9p0 or (
+            pa_version_under13p0 and all_numeric_accumulations != "cumsum"
+        ):
             # xfailing takes a long time to run because pytest
             # renders the exception messages even when not showing them
             opt = request.config.option