diff --git a/python/pyarrow/tests/parquet/common.py b/python/pyarrow/tests/parquet/common.py
index 8365ed5b28543..c3094ee20b34c 100644
--- a/python/pyarrow/tests/parquet/common.py
+++ b/python/pyarrow/tests/parquet/common.py
@@ -83,7 +83,7 @@ def _random_integers(size, dtype):
     iinfo = np.iinfo(dtype)
     return np.random.randint(max(iinfo.min, platform_int_info.min),
                              min(iinfo.max, platform_int_info.max),
-                             size=size).astype(dtype)
+                             size=size, dtype=dtype)
 
 
 def _range_integers(size, dtype):
diff --git a/python/pyarrow/tests/test_array.py b/python/pyarrow/tests/test_array.py
index 88394c77e429d..1032ab9add3ca 100644
--- a/python/pyarrow/tests/test_array.py
+++ b/python/pyarrow/tests/test_array.py
@@ -3398,7 +3398,7 @@ def test_numpy_array_protocol():
     result = np.asarray(arr)
     np.testing.assert_array_equal(result, expected)
 
-    if Version(np.__version__) < Version("2.0"):
+    if Version(np.__version__) < Version("2.0.0.dev0"):
         # copy keyword is not strict and not passed down to __array__
         result = np.array(arr, copy=False)
         np.testing.assert_array_equal(result, expected)
diff --git a/python/pyarrow/tests/test_pandas.py b/python/pyarrow/tests/test_pandas.py
index be2c5b14e68b0..ba9d6a3c01391 100644
--- a/python/pyarrow/tests/test_pandas.py
+++ b/python/pyarrow/tests/test_pandas.py
@@ -780,7 +780,7 @@ def test_integer_no_nulls(self):
             info = np.iinfo(dtype)
             values = np.random.randint(max(info.min, np.iinfo(np.int_).min),
                                        min(info.max, np.iinfo(np.int_).max),
-                                       size=num_values)
+                                       size=num_values, dtype=dtype)
             data[dtype] = values.astype(dtype)
             fields.append(pa.field(dtype, arrow_dtype))
 
diff --git a/python/pyarrow/tests/test_table.py b/python/pyarrow/tests/test_table.py
index a58010d083e92..f40759de50c8c 100644
--- a/python/pyarrow/tests/test_table.py
+++ b/python/pyarrow/tests/test_table.py
@@ -3281,7 +3281,7 @@ def test_numpy_array_protocol(constructor):
     table = constructor([[1, 2, 3], [4.0, 5.0, 6.0]], names=["a", "b"])
     expected = np.array([[1, 4], [2, 5], [3, 6]], dtype="float64")
 
-    if Version(np.__version__) < Version("2.0"):
+    if Version(np.__version__) < Version("2.0.0.dev0"):
         # copy keyword is not strict and not passed down to __array__
         result = np.array(table, copy=False)
         np.testing.assert_array_equal(result, expected)
diff --git a/python/scripts/test_leak.py b/python/scripts/test_leak.py
index f2bbe8d051bf9..86a87f5e742e8 100644
--- a/python/scripts/test_leak.py
+++ b/python/scripts/test_leak.py
@@ -98,7 +98,7 @@ def func():
 
 
 def test_ARROW_8801():
-    x = pd.to_datetime(np.random.randint(0, 2**32, size=2**20),
+    x = pd.to_datetime(np.random.randint(0, 2**32, size=2**20, dtype=np.int64),
                        unit='ms', utc=True)
     table = pa.table(pd.DataFrame({'x': x}))