diff --git a/doc/whats-new.rst b/doc/whats-new.rst
index 4b5bb1e491f..2cd4284f3cb 100644
--- a/doc/whats-new.rst
+++ b/doc/whats-new.rst
@@ -70,8 +70,8 @@ New Features
   :py:meth:`Dataset.idxmax`, :py:meth:`Dataset.idxmin`.  (:issue:`60`, :pull:`3871`)
   By `Todd Jennings <https://github.com/toddrjen>`_
 - Support dask handling for :py:meth:`DataArray.idxmax`, :py:meth:`DataArray.idxmin`,
-  :py:meth:`Dataset.idxmax`, :py:meth:`Dataset.idxmin`.  (:pull:`3922`)
-  By `Kai Mühlbauer <https://github.com/kmuehlbauer>`_.
+  :py:meth:`Dataset.idxmax`, :py:meth:`Dataset.idxmin`.  (:pull:`3922`, :pull:`4135`)
+  By `Kai Mühlbauer <https://github.com/kmuehlbauer>`_ and `Pascal Bourgault <https://github.com/aulemahal>`_.
 - More support for unit aware arrays with pint (:pull:`3643`, :pull:`3975`)
   By `Justus Magin <https://github.com/keewis>`_.
 - Support overriding existing variables in ``to_zarr()`` with ``mode='a'`` even
diff --git a/xarray/core/computation.py b/xarray/core/computation.py
index cecd4fd8e70..4f4fd475c82 100644
--- a/xarray/core/computation.py
+++ b/xarray/core/computation.py
@@ -1563,7 +1563,7 @@ def _calc_idxminmax(
 
         chunks = dict(zip(array.dims, array.chunks))
         dask_coord = dask.array.from_array(array[dim].data, chunks=chunks[dim])
-        res = indx.copy(data=dask_coord[(indx.data,)])
+        res = indx.copy(data=dask_coord[indx.data.ravel()].reshape(indx.shape))
         # we need to attach back the dim name
         res.name = dim
     else:
diff --git a/xarray/tests/test_dataarray.py b/xarray/tests/test_dataarray.py
index 8fc37ac458d..d942667a4c7 100644
--- a/xarray/tests/test_dataarray.py
+++ b/xarray/tests/test_dataarray.py
@@ -5257,6 +5257,25 @@ def test_idxmax(self, x, minindex, maxindex, nanindex, use_dask):
         assert_identical(result7, expected7)
 
 
+class TestReduceND(TestReduce):
+    @pytest.mark.parametrize("op", ["idxmin", "idxmax"])
+    @pytest.mark.parametrize("ndim", [3, 5])
+    def test_idxminmax_dask(self, op, ndim):
+        if not has_dask:
+            pytest.skip("requires dask")
+
+        ar0_raw = xr.DataArray(
+            np.random.random_sample(size=[10] * ndim),
+            dims=[i for i in "abcdefghij"[: ndim - 1]] + ["x"],
+            coords={"x": np.arange(10)},
+            attrs=self.attrs,
+        )
+
+        ar0_dsk = ar0_raw.chunk({})
+        # Assert idx is the same with dask and without
+        assert_equal(getattr(ar0_dsk, op)(dim="x"), getattr(ar0_raw, op)(dim="x"))
+
+
 @pytest.fixture(params=[1])
 def da(request):
     if request.param == 1: