diff --git a/cpp/src/arrow/compute/kernels/scalar_cast_extension.cc b/cpp/src/arrow/compute/kernels/scalar_cast_extension.cc
index c32a6ef6de93e..2a54d28c6fb64 100644
--- a/cpp/src/arrow/compute/kernels/scalar_cast_extension.cc
+++ b/cpp/src/arrow/compute/kernels/scalar_cast_extension.cc
@@ -56,8 +56,9 @@ Status CastToExtension(KernelContext* ctx, const ExecSpan& batch, ExecResult* ou
 std::shared_ptr<CastFunction> GetCastToExtension(std::string name) {
   auto func = std::make_shared<CastFunction>(std::move(name), Type::EXTENSION);
   for (Type::type in_ty : AllTypeIds()) {
-    DCHECK_OK(
-        func->AddKernel(in_ty, {InputType(in_ty)}, kOutputTargetType, CastToExtension));
+    DCHECK_OK(func->AddKernel(in_ty, {InputType(in_ty)}, kOutputTargetType,
+                              CastToExtension, NullHandling::COMPUTED_NO_PREALLOCATE,
+                              MemAllocation::NO_PREALLOCATE));
   }
   return func;
 }
diff --git a/python/pyarrow/tests/test_extension_type.py b/python/pyarrow/tests/test_extension_type.py
index 9863d96058947..1c4d0175a2d97 100644
--- a/python/pyarrow/tests/test_extension_type.py
+++ b/python/pyarrow/tests/test_extension_type.py
@@ -194,6 +194,21 @@ def __arrow_ext_deserialize__(cls, storage_type, serialized):
         return cls(storage_type)
 
 
+class MyFixedListType(pa.ExtensionType):
+
+    def __init__(self, storage_type):
+        assert isinstance(storage_type, pa.FixedSizeListType)
+        super().__init__(storage_type, 'pyarrow.tests.MyFixedListType')
+
+    def __arrow_ext_serialize__(self):
+        return b''
+
+    @classmethod
+    def __arrow_ext_deserialize__(cls, storage_type, serialized):
+        assert serialized == b''
+        return cls(storage_type)
+
+
 class AnnotatedType(pa.ExtensionType):
     """
     Generic extension type that can store any storage type.
@@ -738,6 +753,36 @@ def test_casting_dict_array_to_extension_type():
                                UUID('30313233-3435-3637-3839-616263646566')]
 
 
+def test_cast_to_extension_with_nested_storage():
+    # https://github.com/apache/arrow/issues/37669
+
+    # With fixed-size list
+    array = pa.array([[1, 2], [3, 4], [5, 6]], pa.list_(pa.float64(), 2))
+    result = array.cast(MyFixedListType(pa.list_(pa.float64(), 2)))
+    expected = pa.ExtensionArray.from_storage(MyFixedListType(array.type), array)
+    assert result.equals(expected)
+
+    ext_type = MyFixedListType(pa.list_(pa.float32(), 2))
+    result = array.cast(ext_type)
+    expected = pa.ExtensionArray.from_storage(
+        ext_type, array.cast(ext_type.storage_type)
+    )
+    assert result.equals(expected)
+
+    # With variable-size list
+    array = pa.array([[1, 2], [3], [4, 5, 6]], pa.list_(pa.float64()))
+    result = array.cast(MyListType(pa.list_(pa.float64())))
+    expected = pa.ExtensionArray.from_storage(MyListType(array.type), array)
+    assert result.equals(expected)
+
+    ext_type = MyListType(pa.list_(pa.float32()))
+    result = array.cast(ext_type)
+    expected = pa.ExtensionArray.from_storage(
+        ext_type, array.cast(ext_type.storage_type)
+    )
+    assert result.equals(expected)
+
+
 def test_concat():
     arr1 = pa.array([1, 2, 3], IntegerType())
     arr2 = pa.array([4, 5, 6], IntegerType())
@@ -1500,6 +1545,21 @@ def test_tensor_type_equality():
     assert not tensor_type == tensor_type3
 
 
+def test_tensor_type_cast():
+    tensor_type = pa.fixed_shape_tensor(pa.int8(), [2, 3])
+    inner = pa.array(range(18), pa.int8())
+    storage = pa.FixedSizeListArray.from_arrays(inner, 6)
+
+    # cast storage -> extension type
+    result = storage.cast(tensor_type)
+    expected = pa.ExtensionArray.from_storage(tensor_type, storage)
+    assert result.equals(expected)
+
+    # cast extension type -> storage type
+    storage_result = result.cast(storage.type)
+    assert storage_result.equals(storage)
+
+
 @pytest.mark.pandas
 def test_extension_to_pandas_storage_type(registered_period_type):
     period_type, _ = registered_period_type