diff --git a/xarray/core/extension_array.py b/xarray/core/extension_array.py
index 096a427e425..f1631a5ea9e 100644
--- a/xarray/core/extension_array.py
+++ b/xarray/core/extension_array.py
@@ -1,5 +1,6 @@
 from __future__ import annotations
 
+import copy
 from collections.abc import Callable, Sequence
 from dataclasses import dataclass
 from typing import Any, Generic, cast
@@ -148,4 +149,14 @@ def __getattr__(self, attr: str) -> Any:
         # Thus, if we didn't have `super().__getattribute__("array")` this method would call `self.array` (i.e., `getattr(self, "array")`) again while looking for `__setstate__`
         # (which is apparently the first thing sought in copy.copy from the under-construction copied object),
         # which would cause a recursion error since `array` is not present on the object when it is being constructed during `__{deep}copy__`.
+        # Even though we have defined these two methods now below due to `test_extension_array_copy_arrow_type` (cause unknown)
+        # we leave this here as it more robust than self.array
         return getattr(super().__getattribute__("array"), attr)
+
+    def __copy__(self) -> PandasExtensionArray[T_ExtensionArray]:
+        return PandasExtensionArray(copy.copy(self.array))
+
+    def __deepcopy__(
+        self, memo: dict[int, Any] | None = None
+    ) -> PandasExtensionArray[T_ExtensionArray]:
+        return PandasExtensionArray(copy.deepcopy(self.array, memo=memo))
diff --git a/xarray/tests/test_duck_array_ops.py b/xarray/tests/test_duck_array_ops.py
index 4052d414f63..eaafe2d4536 100644
--- a/xarray/tests/test_duck_array_ops.py
+++ b/xarray/tests/test_duck_array_ops.py
@@ -1,5 +1,6 @@
 from __future__ import annotations
 
+import copy
 import datetime as dt
 import pickle
 import warnings
@@ -200,6 +201,16 @@ def test_extension_array_pyarrow_concatenate(self, arrow1, arrow2):
         assert concatenated[2].array[0]["x"] == 3
         assert concatenated[3].array[0]["y"]
 
+    @requires_pyarrow
+    def test_extension_array_copy_arrow_type(self):
+        arr = pd.array([pd.NA, 1, 2], dtype="int64[pyarrow]")
+        # Relying on the `__getattr__` of `PandasExtensionArray` to do the deep copy
+        # recursively only fails for `int64[pyarrow]` and similar types so this
+        # test ensures that copying still works there.
+        assert isinstance(
+            copy.deepcopy(PandasExtensionArray(arr), memo=None).array, type(arr)
+        )
+
     def test___getitem__extension_duck_array(self, categorical1):
         extension_duck_array = PandasExtensionArray(categorical1)
         assert (extension_duck_array[0:2] == categorical1[0:2]).all()