diff --git a/xarray/namedarray/parallelcompat.py b/xarray/namedarray/parallelcompat.py
index c6263bff4ff..c923e55db8b 100644
--- a/xarray/namedarray/parallelcompat.py
+++ b/xarray/namedarray/parallelcompat.py
@@ -121,11 +121,13 @@ def guess_chunkmanager(
         )
 
 
-def get_chunked_array_type(*args: Any) -> ChunkManagerEntrypoint[Any]:
+def get_chunked_array_type(*args: Any) -> ChunkManagerEntrypoint[Any] | None:
     """
     Detects which parallel backend should be used for given set of arrays.
 
     Also checks that all arrays are of same chunking type (i.e. not a mix of cubed and dask).
+
+    Returns None if no matching ChunkManager is found.
     """
 
     # TODO this list is probably redundant with something inside xarray.apply_ufunc
@@ -155,9 +157,7 @@ def get_chunked_array_type(*args: Any) -> ChunkManagerEntrypoint[Any]:
         if chunkmanager.is_chunked_array(chunked_arr)
     ]
     if not selected:
-        raise TypeError(
-            f"Could not find a Chunk Manager which recognises type {type(chunked_arr)}"
-        )
+        return None
     elif len(selected) >= 2:
         raise TypeError(f"Multiple ChunkManagers recognise type {type(chunked_arr)}")
     else:
diff --git a/xarray/namedarray/pycompat.py b/xarray/namedarray/pycompat.py
index 3ce33d4d8ea..84854ffb33a 100644
--- a/xarray/namedarray/pycompat.py
+++ b/xarray/namedarray/pycompat.py
@@ -108,7 +108,8 @@ def to_numpy(
     # TODO first attempt to call .to_numpy() once some libraries implement it
     if is_chunked_array(data):
         chunkmanager = get_chunked_array_type(data)
-        data, *_ = chunkmanager.compute(data, **kwargs)
+        if chunkmanager is not None:
+            data, *_ = chunkmanager.compute(data, **kwargs)
     if isinstance(data, array_type("cupy")):
         data = data.get()
     # pint has to be imported dynamically as pint imports xarray
@@ -127,8 +128,9 @@ def to_duck_array(data: Any, **kwargs: dict[str, Any]) -> duckarray[_ShapeType,
 
     if is_chunked_array(data):
         chunkmanager = get_chunked_array_type(data)
-        loaded_data, *_ = chunkmanager.compute(data, **kwargs)  # type: ignore[var-annotated]
-        return loaded_data
+        if chunkmanager is not None:
+            loaded_data, *_ = chunkmanager.compute(data, **kwargs)  # type: ignore[var-annotated]
+            return loaded_data
 
     if isinstance(data, ExplicitlyIndexed):
         return data.get_duck_array()  # type: ignore[no-untyped-call, no-any-return]
diff --git a/xarray/tests/test_parallelcompat.py b/xarray/tests/test_parallelcompat.py
index d4a4e273bc0..a96ed31c04b 100644
--- a/xarray/tests/test_parallelcompat.py
+++ b/xarray/tests/test_parallelcompat.py
@@ -195,10 +195,7 @@ def test_raise_if_no_arrays_chunked(self, register_dummy_chunkmanager) -> None:
     def test_raise_if_no_matching_chunkmanagers(self) -> None:
         dummy_arr = DummyChunkedArray([1, 2, 3])
 
-        with pytest.raises(
-            TypeError, match="Could not find a Chunk Manager which recognises"
-        ):
-            get_chunked_array_type(dummy_arr)
+        assert get_chunked_array_type(dummy_arr) is None
 
     @requires_dask
     def test_detect_dask_if_installed(self) -> None:
diff --git a/xarray/tests/test_variable.py b/xarray/tests/test_variable.py
index 6575f2e1740..12a170ad75e 100644
--- a/xarray/tests/test_variable.py
+++ b/xarray/tests/test_variable.py
@@ -29,7 +29,7 @@
 from xarray.core.types import T_DuckArray
 from xarray.core.utils import NDArrayMixin
 from xarray.core.variable import as_compatible_data, as_variable
-from xarray.namedarray.pycompat import array_type
+from xarray.namedarray.pycompat import array_type, is_chunked_array
 from xarray.tests import (
     assert_allclose,
     assert_array_equal,
@@ -2722,6 +2722,27 @@ def __init__(self, array):
         orig = Variable(dims=(), data=array)
         assert isinstance(orig._data.item(), CustomWithValuesAttr)
 
+    def test_duck_array_with_chunks(self):
+        # Non indexable type
+        class CustomArray(NDArrayMixin):
+            def __init__(self, array):
+                self.array = array
+
+            @property
+            def chunks(self):
+                return self.shape
+
+            def __array_function__(self, *args, **kwargs):
+                return NotImplemented
+
+            def __array_ufunc__(self, *args, **kwargs):
+                return NotImplemented
+
+        array = CustomArray(np.arange(3))
+        assert is_chunked_array(array)
+        var = Variable(dims=("x"), data=array)
+        var.load()
+
 
 def test_raise_no_warning_for_nan_in_binary_ops():
     with assert_no_warnings():