diff --git a/python/pyarrow/pandas_compat.py b/python/pyarrow/pandas_compat.py
index 7fbde36bc23e9..5a930a41f0300 100644
--- a/python/pyarrow/pandas_compat.py
+++ b/python/pyarrow/pandas_compat.py
@@ -848,6 +848,25 @@ def _get_extension_dtypes(table, columns_metadata, types_mapper=None):
     if _pandas_api.extension_dtype is None:
         return ext_columns
 
+    # use the specified mapping of built-in arrow types to pandas dtypes
+    if types_mapper:
+        for field in table.schema:
+            typ = field.type
+            pandas_dtype = types_mapper(typ)
+            if pandas_dtype is not None:
+                ext_columns[field.name] = pandas_dtype
+
+    # infer from extension type in the schema
+    for field in table.schema:
+        typ = field.type
+        if field.name not in ext_columns and isinstance(typ, pa.BaseExtensionType):
+            try:
+                pandas_dtype = typ.to_pandas_dtype()
+            except NotImplementedError:
+                pass
+            else:
+                ext_columns[field.name] = pandas_dtype
+
     # infer the extension columns from the pandas metadata
     for col_meta in columns_metadata:
         try:
@@ -856,7 +875,7 @@ def _get_extension_dtypes(table, columns_metadata, types_mapper=None):
             name = col_meta['name']
         dtype = col_meta['numpy_type']
 
-        if dtype not in _pandas_supported_numpy_types:
+        if name not in ext_columns and dtype not in _pandas_supported_numpy_types:
             # pandas_dtype is expensive, so avoid doing this for types
             # that are certainly numpy dtypes
             pandas_dtype = _pandas_api.pandas_dtype(dtype)
@@ -864,25 +883,6 @@ def _get_extension_dtypes(table, columns_metadata, types_mapper=None):
                 if hasattr(pandas_dtype, "__from_arrow__"):
                     ext_columns[name] = pandas_dtype
 
-    # infer from extension type in the schema
-    for field in table.schema:
-        typ = field.type
-        if isinstance(typ, pa.BaseExtensionType):
-            try:
-                pandas_dtype = typ.to_pandas_dtype()
-            except NotImplementedError:
-                pass
-            else:
-                ext_columns[field.name] = pandas_dtype
-
-    # use the specified mapping of built-in arrow types to pandas dtypes
-    if types_mapper:
-        for field in table.schema:
-            typ = field.type
-            pandas_dtype = types_mapper(typ)
-            if pandas_dtype is not None:
-                ext_columns[field.name] = pandas_dtype
-
     return ext_columns
 
 
diff --git a/python/pyarrow/tests/test_pandas.py b/python/pyarrow/tests/test_pandas.py
index 178a073ed59dc..1186f87b0322a 100644
--- a/python/pyarrow/tests/test_pandas.py
+++ b/python/pyarrow/tests/test_pandas.py
@@ -4411,6 +4411,31 @@ def test_to_pandas_extension_dtypes_mapping():
     assert isinstance(result['a'].dtype, pd.PeriodDtype)
 
 
+def test_to_pandas_extension_dtypes_mapping_complex_type():
+    # https://github.com/apache/arrow/pull/44720
+    if Version(pd.__version__) < Version("1.5.2"):
+        pytest.skip("Test relies on pd.ArrowDtype")
+    pa_type = pa.struct(
+        [
+            pa.field("bar", pa.bool_(), nullable=False),
+            pa.field("baz", pa.float32(), nullable=True),
+        ],
+    )
+    pd_type = pd.ArrowDtype(pa_type)
+    schema = pa.schema([pa.field("foo", pa_type)])
+    df0 = pd.DataFrame(
+        [
+            {"foo": {"bar": True, "baz": np.float32(1)}},
+            {"foo": {"bar": True, "baz": None}},
+        ],
+    ).astype({"foo": pd_type})
+
+    # Round trip df0 into df1
+    table = pa.Table.from_pandas(df0, schema=schema)
+    df1 = table.to_pandas(types_mapper=pd.ArrowDtype)
+    pd.testing.assert_frame_equal(df0, df1)
+
+
 def test_array_to_pandas():
     if Version(pd.__version__) < Version("1.1"):
         pytest.skip("ExtensionDtype to_pandas method missing")