diff --git a/doc/whats-new.rst b/doc/whats-new.rst
index 5ff3ff20b6a..667e75de0b4 100644
--- a/doc/whats-new.rst
+++ b/doc/whats-new.rst
@@ -44,6 +44,9 @@ New Features
   By `Thomas Hirtz <https://github.com/thomashirtz>`_.
 - allow passing a function to ``combine_attrs`` (:pull:`4896`).
   By `Justus Magin <https://github.com/keewis>`_.
+- The values stored in an dataarray can now be referenced in a call to
+  py:func:`xarray.DataArray.query` via 'self' (:issue:`5492`, :pull:`5493`).
+  By `Tom Nicholas <https://github.com/TomNicholas>`_.
 
 Breaking changes
 ~~~~~~~~~~~~~~~~
@@ -73,6 +76,9 @@ Bug fixes
 - Fix the ``repr`` of :py:class:`Variable` objects with ``display_expand_data=True``
   (:pull:`5406`)
   By `Justus Magin <https://github.com/keewis>`_.
+- Fixed :py:func:`xarray.DataArray.query` to not fail with an unnamed dataarray
+  (:issue:`5492`, :pull:`5493`).
+  By `Tom Nicholas <https://github.com/TomNicholas>`_.
 
 
 Documentation
diff --git a/xarray/core/dataarray.py b/xarray/core/dataarray.py
index eab4413d5ce..ed0dcd45500 100644
--- a/xarray/core/dataarray.py
+++ b/xarray/core/dataarray.py
@@ -4437,6 +4437,8 @@ def query(
         dimension(s), where the indexers are given as strings containing
         Python expressions to be evaluated against the values in the array.
 
+        The values stored in dataarrays can also be referenced in queries as 'self'.
+
         Parameters
         ----------
         queries : dict, optional
@@ -4488,17 +4490,43 @@ def query(
         <xarray.DataArray 'a' (x: 2)>
         array([3, 4])
         Dimensions without coordinates: x
+
+        >>> da = xr.DataArray(np.arange(0, 5, 1), dims="x", name=None)
+        >>> da
+        <xarray.DataArray (x: 5)>
+        array([0, 1, 2, 3, 4])
+        Dimensions without coordinates: x
+        >>> da.query(x="self > 2")
+        <xarray.DataArray (x: 2)>
+        array([3, 4])
+        Dimensions without coordinates: x
         """
 
-        ds = self._to_dataset_whole(shallow_copy=True)
-        ds = ds.query(
+        if self.name is None:
+            # Naming unnamed dataarrays as 'self' allows querying their values still
+            name = "self"
+        else:
+            # For consistency allow named datarrays to be referred to as 'self' also
+            name = self.name
+            queries = either_dict_or_kwargs(queries, queries_kwargs, "query")
+            queries = {
+                d: (q.replace("self", name) if isinstance(q, str) else q)
+                for d, q in queries.items()
+            }
+            queries_kwargs = {}
+
+        ds = self._to_dataset_whole(name=name).query(
             queries=queries,
             parser=parser,
             engine=engine,
             missing_dims=missing_dims,
             **queries_kwargs,
         )
-        return ds[self.name]
+
+        da = ds[name]
+        if name == "self":
+            da.name = None
+        return da
 
     def curvefit(
         self,
diff --git a/xarray/tests/test_dataarray.py b/xarray/tests/test_dataarray.py
index 95b6036712c..a0b7afc8786 100644
--- a/xarray/tests/test_dataarray.py
+++ b/xarray/tests/test_dataarray.py
@@ -4659,6 +4659,8 @@ def test_query(self, backend, engine, parser):
             bb = DataArray(data=b, dims=["x"], name="b")
             cc = DataArray(data=c, dims=["y"], name="c")
             dd = DataArray(data=d, dims=["z"], name="d")
+            nn = DataArray(data=a, dims=["x"])
+            nn.name = None
 
         elif backend == "dask":
             import dask.array as da
@@ -4667,6 +4669,8 @@ def test_query(self, backend, engine, parser):
             bb = DataArray(data=da.from_array(b, chunks=3), dims=["x"], name="b")
             cc = DataArray(data=da.from_array(c, chunks=7), dims=["y"], name="c")
             dd = DataArray(data=da.from_array(d, chunks=12), dims=["z"], name="d")
+            nn = DataArray(data=da.from_array(a, chunks=3), dims=["x"])
+            nn.name = None
 
         # query single dim, single variable
         actual = aa.query(x="a > 5", engine=engine, parser=parser)
@@ -4704,6 +4708,16 @@ def test_query(self, backend, engine, parser):
         with pytest.raises(UndefinedVariableError):
             aa.query(x="spam > 50")  # name not present
 
+        # test with nameless dataarray (GH issue 5492)
+        actual = nn.query(x="self > 5", engine=engine, parser=parser)
+        expect = nn.isel(x=(nn > 5))
+        assert_identical(expect, actual)
+
+        # test referring to named dataarray as self
+        actual = aa.query(x="self > 5", engine=engine, parser=parser)
+        expect = aa.isel(x=(aa > 5))
+        assert_identical(expect, actual)
+
     @requires_scipy
     @pytest.mark.parametrize("use_dask", [True, False])
     def test_curvefit(self, use_dask):