diff --git a/doc/whats-new.rst b/doc/whats-new.rst
index cc3bf5ca410..f4dea1cd2aa 100644
--- a/doc/whats-new.rst
+++ b/doc/whats-new.rst
@@ -37,6 +37,9 @@ Deprecations
 Bug fixes
 ~~~~~~~~~
 
+- Allow accessing arbitrary attributes on Pandas ExtensionArrays.
+  By `Deepak Cherian <https://github.com/dcherian>`_.
+
 
 Documentation
 ~~~~~~~~~~~~~
diff --git a/xarray/core/extension_array.py b/xarray/core/extension_array.py
index 269016ddfd1..096a427e425 100644
--- a/xarray/core/extension_array.py
+++ b/xarray/core/extension_array.py
@@ -2,7 +2,7 @@
 
 from collections.abc import Callable, Sequence
 from dataclasses import dataclass
-from typing import Generic, cast
+from typing import Any, Generic, cast
 
 import numpy as np
 import pandas as pd
@@ -142,3 +142,10 @@ def __array__(
             return np.asarray(self.array, dtype=dtype, copy=copy)
         else:
             return np.asarray(self.array, dtype=dtype)
+
+    def __getattr__(self, attr: str) -> Any:
+        #  with __deepcopy__ or __copy__, the object is first constructed and then the sub-objects are attached (see https://docs.python.org/3/library/copy.html)
+        # 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__`.
+        return getattr(super().__getattribute__("array"), attr)
diff --git a/xarray/tests/test_dataset.py b/xarray/tests/test_dataset.py
index af7db7294a8..11f9e88c69b 100644
--- a/xarray/tests/test_dataset.py
+++ b/xarray/tests/test_dataset.py
@@ -297,7 +297,7 @@ def test_repr(self) -> None:
                 var1     (dim1, dim2) float64 576B -0.9891 -0.3678 1.288 ... -0.2116 0.364
                 var2     (dim1, dim2) float64 576B 0.953 1.52 1.704 ... 0.1347 -0.6423
                 var3     (dim3, dim1) float64 640B 0.4107 0.9941 0.1665 ... 0.716 1.555
-                var4     (dim1) category 64B 'b' 'c' 'b' 'a' 'c' 'a' 'c' 'a'
+                var4     (dim1) category 32B 'b' 'c' 'b' 'a' 'c' 'a' 'c' 'a'
             Attributes:
                 foo:      bar""".format(
                 data["dim3"].dtype,
diff --git a/xarray/tests/test_duck_array_ops.py b/xarray/tests/test_duck_array_ops.py
index ff84041f8f1..4052d414f63 100644
--- a/xarray/tests/test_duck_array_ops.py
+++ b/xarray/tests/test_duck_array_ops.py
@@ -1,6 +1,7 @@
 from __future__ import annotations
 
 import datetime as dt
+import pickle
 import warnings
 
 import numpy as np
@@ -1094,3 +1095,19 @@ def test_extension_array_singleton_equality(categorical1):
 def test_extension_array_repr(int1):
     int_duck_array = PandasExtensionArray(int1)
     assert repr(int1) in repr(int_duck_array)
+
+
+def test_extension_array_attr():
+    array = pd.Categorical(["cat2", "cat1", "cat2", "cat3", "cat1"])
+    wrapped = PandasExtensionArray(array)
+    assert_array_equal(array.categories, wrapped.categories)
+    assert array.nbytes == wrapped.nbytes
+
+    roundtripped = pickle.loads(pickle.dumps(wrapped))
+    assert isinstance(roundtripped, PandasExtensionArray)
+    assert (roundtripped == wrapped).all()
+
+    interval_array = pd.arrays.IntervalArray.from_breaks([0, 1, 2, 3], closed="right")
+    wrapped = PandasExtensionArray(interval_array)
+    assert_array_equal(wrapped.left, interval_array.left, strict=True)
+    assert wrapped.closed == interval_array.closed