diff --git a/doc/api.rst b/doc/api.rst
index ceab7dcc976..9cb02441d37 100644
--- a/doc/api.rst
+++ b/doc/api.rst
@@ -126,6 +126,7 @@ Indexing
    Dataset.isel
    Dataset.sel
    Dataset.drop_sel
+   Dataset.drop_isel
    Dataset.head
    Dataset.tail
    Dataset.thin
@@ -307,6 +308,7 @@ Indexing
    DataArray.isel
    DataArray.sel
    DataArray.drop_sel
+   DataArray.drop_isel
    DataArray.head
    DataArray.tail
    DataArray.thin
diff --git a/doc/whats-new.rst b/doc/whats-new.rst
index 88994a5bfc0..717a40f37ec 100644
--- a/doc/whats-new.rst
+++ b/doc/whats-new.rst
@@ -80,6 +80,7 @@ Bug fixes
 - Expand user directory paths (e.g. ``~/``) in :py:func:`open_mfdataset` and
   :py:meth:`Dataset.to_zarr` (:issue:`4783`, :pull:`4795`).
   By `Julien Seguinot <https://github.com/juseg>`_.
+- Add :py:meth:`Dataset.drop_isel` and :py:meth:`DataArray.drop_isel` (:issue:`4658`, :pull:`4819`). By `Daniel Mesejo <https://github.com/mesejo>`_.
 
 Documentation
 ~~~~~~~~~~~~~
diff --git a/xarray/core/dataarray.py b/xarray/core/dataarray.py
index 6fdda8fc418..ed645c06e27 100644
--- a/xarray/core/dataarray.py
+++ b/xarray/core/dataarray.py
@@ -2247,6 +2247,28 @@ def drop_sel(
         ds = self._to_temp_dataset().drop_sel(labels, errors=errors)
         return self._from_temp_dataset(ds)
 
+    def drop_isel(self, indexers=None, **indexers_kwargs):
+        """Drop index positions from this DataArray.
+
+        Parameters
+        ----------
+        indexers : mapping of hashable to Any
+            Index locations to drop
+        **indexers_kwargs : {dim: position, ...}, optional
+            The keyword arguments form of ``dim`` and ``positions``
+
+        Returns
+        -------
+        dropped : DataArray
+
+        Raises
+        ------
+        IndexError
+        """
+        dataset = self._to_temp_dataset()
+        dataset = dataset.drop_isel(indexers=indexers, **indexers_kwargs)
+        return self._from_temp_dataset(dataset)
+
     def dropna(
         self, dim: Hashable, how: str = "any", thresh: int = None
     ) -> "DataArray":
diff --git a/xarray/core/dataset.py b/xarray/core/dataset.py
index 7edc2fab067..65f38a7e26a 100644
--- a/xarray/core/dataset.py
+++ b/xarray/core/dataset.py
@@ -4053,13 +4053,78 @@ def drop_sel(self, labels=None, *, errors="raise", **labels_kwargs):
                 labels_for_dim = [labels_for_dim]
             labels_for_dim = np.asarray(labels_for_dim)
             try:
-                index = self.indexes[dim]
+                index = self.get_index(dim)
             except KeyError:
                 raise ValueError("dimension %r does not have coordinate labels" % dim)
             new_index = index.drop(labels_for_dim, errors=errors)
             ds = ds.loc[{dim: new_index}]
         return ds
 
+    def drop_isel(self, indexers=None, **indexers_kwargs):
+        """Drop index positions from this Dataset.
+
+        Parameters
+        ----------
+        indexers : mapping of hashable to Any
+            Index locations to drop
+        **indexers_kwargs : {dim: position, ...}, optional
+            The keyword arguments form of ``dim`` and ``positions``
+
+        Returns
+        -------
+        dropped : Dataset
+
+        Raises
+        ------
+        IndexError
+
+        Examples
+        --------
+        >>> data = np.arange(6).reshape(2, 3)
+        >>> labels = ["a", "b", "c"]
+        >>> ds = xr.Dataset({"A": (["x", "y"], data), "y": labels})
+        >>> ds
+        <xarray.Dataset>
+        Dimensions:  (x: 2, y: 3)
+        Coordinates:
+          * y        (y) <U1 'a' 'b' 'c'
+        Dimensions without coordinates: x
+        Data variables:
+            A        (x, y) int64 0 1 2 3 4 5
+        >>> ds.drop_isel(y=[0, 2])
+        <xarray.Dataset>
+        Dimensions:  (x: 2, y: 1)
+        Coordinates:
+          * y        (y) <U1 'b'
+        Dimensions without coordinates: x
+        Data variables:
+            A        (x, y) int64 1 4
+        >>> ds.drop_isel(y=1)
+        <xarray.Dataset>
+        Dimensions:  (x: 2, y: 2)
+        Coordinates:
+          * y        (y) <U1 'a' 'c'
+        Dimensions without coordinates: x
+        Data variables:
+            A        (x, y) int64 0 2 3 5
+        """
+
+        indexers = either_dict_or_kwargs(indexers, indexers_kwargs, "drop")
+
+        ds = self
+        dimension_index = {}
+        for dim, pos_for_dim in indexers.items():
+            # Don't cast to set, as it would harm performance when labels
+            # is a large numpy array
+            if utils.is_scalar(pos_for_dim):
+                pos_for_dim = [pos_for_dim]
+            pos_for_dim = np.asarray(pos_for_dim)
+            index = self.get_index(dim)
+            new_index = index.delete(pos_for_dim)
+            dimension_index[dim] = new_index
+        ds = ds.loc[dimension_index]
+        return ds
+
     def drop_dims(
         self, drop_dims: Union[Hashable, Iterable[Hashable]], *, errors: str = "raise"
     ) -> "Dataset":
diff --git a/xarray/tests/test_dataarray.py b/xarray/tests/test_dataarray.py
index 3ead427e22e..afb234029dc 100644
--- a/xarray/tests/test_dataarray.py
+++ b/xarray/tests/test_dataarray.py
@@ -2327,6 +2327,12 @@ def test_drop_index_labels(self):
         with pytest.warns(DeprecationWarning):
             arr.drop([0, 1, 3], dim="y", errors="ignore")
 
+    def test_drop_index_positions(self):
+        arr = DataArray(np.random.randn(2, 3), dims=["x", "y"])
+        actual = arr.drop_sel(y=[0, 1])
+        expected = arr[:, 2:]
+        assert_identical(actual, expected)
+
     def test_dropna(self):
         x = np.random.randn(4, 4)
         x[::2, 0] = np.nan
diff --git a/xarray/tests/test_dataset.py b/xarray/tests/test_dataset.py
index bd1938455b1..f71b8ec7741 100644
--- a/xarray/tests/test_dataset.py
+++ b/xarray/tests/test_dataset.py
@@ -2371,8 +2371,12 @@ def test_drop_index_labels(self):
             data.drop(DataArray(["a", "b", "c"]), dim="x", errors="ignore")
         assert_identical(expected, actual)
 
-        with raises_regex(ValueError, "does not have coordinate labels"):
-            data.drop_sel(y=1)
+        actual = data.drop_sel(y=[1])
+        expected = data.isel(y=[0, 2])
+        assert_identical(expected, actual)
+
+        with raises_regex(KeyError, "not found in axis"):
+            data.drop_sel(x=0)
 
     def test_drop_labels_by_keyword(self):
         data = Dataset(
@@ -2410,6 +2414,34 @@ def test_drop_labels_by_keyword(self):
         with pytest.raises(ValueError):
             data.drop(dim="x", x="a")
 
+    def test_drop_labels_by_position(self):
+        data = Dataset(
+            {"A": (["x", "y"], np.random.randn(2, 6)), "x": ["a", "b"], "y": range(6)}
+        )
+        # Basic functionality.
+        assert len(data.coords["x"]) == 2
+
+        actual = data.drop_isel(x=0)
+        expected = data.drop_sel(x="a")
+        assert_identical(expected, actual)
+
+        actual = data.drop_isel(x=[0])
+        expected = data.drop_sel(x=["a"])
+        assert_identical(expected, actual)
+
+        actual = data.drop_isel(x=[0, 1])
+        expected = data.drop_sel(x=["a", "b"])
+        assert_identical(expected, actual)
+        assert actual.coords["x"].size == 0
+
+        actual = data.drop_isel(x=[0, 1], y=range(0, 6, 2))
+        expected = data.drop_sel(x=["a", "b"], y=range(0, 6, 2))
+        assert_identical(expected, actual)
+        assert actual.coords["x"].size == 0
+
+        with pytest.raises(KeyError):
+            data.drop_isel(z=1)
+
     def test_drop_dims(self):
         data = xr.Dataset(
             {