diff --git a/python/pyarrow/array.pxi b/python/pyarrow/array.pxi
index ccb51b7337817..b48f08f80e514 100644
--- a/python/pyarrow/array.pxi
+++ b/python/pyarrow/array.pxi
@@ -1544,7 +1544,19 @@ cdef class Array(_PandasConvertible):
         return _array_like_to_pandas(self, options, types_mapper=types_mapper)
 
     def __array__(self, dtype=None, copy=None):
-        # TODO honor the copy keyword
+        # TODO honor the copy=True case
+        if copy is False:
+            try:
+                values = self.to_numpy(zero_copy_only=True)
+            except ArrowInvalid as exc:
+                raise ArrowInvalid(
+                    "Unable to avoid a copy while creating a numpy array as requested.\n"
+                    "If using `np.array(obj, copy=False)` replace it with "
+                    "`np.asarray(obj)` to allow a copy when needed"
+                )
+            # values is already a numpy array at this point, but calling np.array(..)
+            # again to handle the `dtype` keyword with a no-copy guarantee
+            return np.array(values, dtype=dtype, copy=False)
         values = self.to_numpy(zero_copy_only=False)
         if dtype is None:
             return values
diff --git a/python/pyarrow/tests/test_array.py b/python/pyarrow/tests/test_array.py
index 0191f15502894..a961166a2982f 100644
--- a/python/pyarrow/tests/test_array.py
+++ b/python/pyarrow/tests/test_array.py
@@ -31,6 +31,7 @@
 
 import pyarrow as pa
 import pyarrow.tests.strategies as past
+from pyarrow.vendored.version import Version
 
 
 def test_total_bytes_allocated():
@@ -3309,9 +3310,34 @@ def test_numpy_array_protocol():
     np.testing.assert_array_equal(result, expected)
 
     # this should not raise a deprecation warning with numpy 2.0+
-    result = np.asarray(arr, copy=False)
+    result = np.array(arr, copy=False)
     np.testing.assert_array_equal(result, expected)
 
+    result = np.array(arr, dtype="int64", copy=False)
+    np.testing.assert_array_equal(result, expected)
+
+    # no zero-copy is possible
+    arr = pa.array([1, 2, None])
+    expected = np.array([1, 2, np.nan], dtype="float64")
+    result = np.asarray(arr)
+    np.testing.assert_array_equal(result, expected)
+
+    if Version(np.__version__) < Version("2.0"):
+        # copy keyword is not strict and not passed down to __array__
+        result = np.array(arr, copy=False)
+        np.testing.assert_array_equal(result, expected)
+
+        result = np.array(arr, dtype="float64", copy=False)
+        np.testing.assert_array_equal(result, expected)
+    else:
+        # starting with numpy 2.0, the copy=False keyword is assumed to be strict
+        with pytest.raises(ValueError, match="Unable to avoid a copy"):
+            np.array(arr, copy=False)
+
+        arr = pa.array([1, 2, 3])
+        with pytest.raises(ValueError):
+            np.array(arr, dtype="float64", copy=False)
+
 
 def test_array_protocol():