diff --git a/doc/whats-new.rst b/doc/whats-new.rst
index 37cf3af85b9..6debcb5ca0d 100644
--- a/doc/whats-new.rst
+++ b/doc/whats-new.rst
@@ -24,7 +24,8 @@ New Features
 
 - Add a ``create_index=True`` parameter to :py:meth:`Dataset.stack` and
   :py:meth:`DataArray.stack` so that the creation of multi-indexes is optional
-  (:pull:`5692`). By `Benoît Bovy <https://github.com/benbovy>`_.
+  (:pull:`5692`).
+  By `Benoît Bovy <https://github.com/benbovy>`_.
 - Multi-index levels are now accessible through their own, regular coordinates
   instead of virtual coordinates (:pull:`5692`).
   By `Benoît Bovy <https://github.com/benbovy>`_.
@@ -33,7 +34,8 @@ Breaking changes
 ~~~~~~~~~~~~~~~~
 
 - The Dataset and DataArray ``rename*`` methods do not implicitly add or drop
-  indexes. (:pull:`5692`). By `Benoît Bovy <https://github.com/benbovy>`_.
+  indexes. (:pull:`5692`).
+  By `Benoît Bovy <https://github.com/benbovy>`_.
 - Many arguments like ``keep_attrs``, ``axis``, and ``skipna`` are now keyword
   only for all reduction operations like ``.mean``.
   By `Deepak Cherian <https://github.com/dcherian>`_, `Jimmy Westling <https://github.com/illviljan>`_.
@@ -47,12 +49,16 @@ Bug fixes
 
 - Set ``skipna=None`` for all ``quantile`` methods (e.g. :py:meth:`Dataset.quantile`) and
   ensure it skips missing values for float dtypes (consistent with other methods). This should
-  not change the behavior (:pull:`6303`). By `Mathias Hauser <https://github.com/mathause>`_.
+  not change the behavior (:pull:`6303`).
+  By `Mathias Hauser <https://github.com/mathause>`_.
 - Many bugs fixed by the explicit indexes refactor, mainly related to multi-index (virtual)
   coordinates. See the corresponding pull-request on GitHub for more details. (:pull:`5692`).
   By `Benoît Bovy <https://github.com/benbovy>`_.
 - Fixed "unhashable type" error trying to read NetCDF file with variable having its 'units'
-  attribute not ``str`` (e.g. ``numpy.ndarray``) (:issue:`6368`). By `Oleh Khoma <https://github.com/okhoma>`_.
+  attribute not ``str`` (e.g. ``numpy.ndarray``) (:issue:`6368`).
+  By `Oleh Khoma <https://github.com/okhoma>`_.
+- Allow fancy indexing of duck dask arrays along multiple dimensions. (:pull:`6414`)
+  By `Justus Magin <https://github.com/keewis>`_.
 
 Documentation
 ~~~~~~~~~~~~~
@@ -65,7 +71,6 @@ Internal Changes
   corresponding pull-request on GitHub for more details. (:pull:`5692`).
   By `Benoît Bovy <https://github.com/benbovy>`_.
 
-.. _whats-new.2022.02.0:
 .. _whats-new.2022.03.0:
 
 v2022.03.0 (2 March 2022)
diff --git a/xarray/core/indexing.py b/xarray/core/indexing.py
index c797e6652de..c8851788c29 100644
--- a/xarray/core/indexing.py
+++ b/xarray/core/indexing.py
@@ -25,13 +25,7 @@
 
 from . import duck_array_ops, nputils, utils
 from .npcompat import DTypeLike
-from .pycompat import (
-    dask_array_type,
-    dask_version,
-    integer_types,
-    is_duck_dask_array,
-    sparse_array_type,
-)
+from .pycompat import dask_version, integer_types, is_duck_dask_array, sparse_array_type
 from .types import T_Xarray
 from .utils import either_dict_or_kwargs, get_valid_numpy_dtype
 
@@ -682,7 +676,7 @@ def as_indexable(array):
         return NumpyIndexingAdapter(array)
     if isinstance(array, pd.Index):
         return PandasIndexingAdapter(array)
-    if isinstance(array, dask_array_type):
+    if is_duck_dask_array(array):
         return DaskIndexingAdapter(array)
     if hasattr(array, "__array_function__"):
         return NdArrayLikeIndexingAdapter(array)
diff --git a/xarray/tests/test_units.py b/xarray/tests/test_units.py
index bc3cc367c0e..c18b7d18c04 100644
--- a/xarray/tests/test_units.py
+++ b/xarray/tests/test_units.py
@@ -31,7 +31,7 @@
 
 # make sure scalars are converted to 0d arrays so quantities can
 # always be treated like ndarrays
-unit_registry = pint.UnitRegistry(force_ndarray=True)
+unit_registry = pint.UnitRegistry(force_ndarray_like=True)
 Quantity = unit_registry.Quantity
 
 
@@ -1837,21 +1837,43 @@ def test_broadcast_equals(self, unit, dtype):
 
         assert expected == actual
 
+    @pytest.mark.parametrize("dask", [False, pytest.param(True, marks=[requires_dask])])
     @pytest.mark.parametrize(
-        "indices",
+        ["variable", "indexers"],
         (
-            pytest.param(4, id="single index"),
-            pytest.param([5, 2, 9, 1], id="multiple indices"),
+            pytest.param(
+                xr.Variable("x", np.linspace(0, 5, 10)),
+                {"x": 4},
+                id="single value-single indexer",
+            ),
+            pytest.param(
+                xr.Variable("x", np.linspace(0, 5, 10)),
+                {"x": [5, 2, 9, 1]},
+                id="multiple values-single indexer",
+            ),
+            pytest.param(
+                xr.Variable(("x", "y"), np.linspace(0, 5, 20).reshape(4, 5)),
+                {"x": 1, "y": 4},
+                id="single value-multiple indexers",
+            ),
+            pytest.param(
+                xr.Variable(("x", "y"), np.linspace(0, 5, 20).reshape(4, 5)),
+                {"x": [0, 1, 2], "y": [0, 2, 4]},
+                id="multiple values-multiple indexers",
+            ),
         ),
     )
-    def test_isel(self, indices, dtype):
-        array = np.linspace(0, 5, 10).astype(dtype) * unit_registry.s
-        variable = xr.Variable("x", array)
+    def test_isel(self, variable, indexers, dask, dtype):
+        if dask:
+            variable = variable.chunk({dim: 2 for dim in variable.dims})
+        quantified = xr.Variable(
+            variable.dims, variable.data.astype(dtype) * unit_registry.s
+        )
 
         expected = attach_units(
-            strip_units(variable).isel(x=indices), extract_units(variable)
+            strip_units(quantified).isel(indexers), extract_units(quantified)
         )
-        actual = variable.isel(x=indices)
+        actual = quantified.isel(indexers)
 
         assert_units_equal(expected, actual)
         assert_identical(expected, actual)