diff --git a/doc/whats-new.rst b/doc/whats-new.rst
index 7a23c055bf5..470635d2184 100644
--- a/doc/whats-new.rst
+++ b/doc/whats-new.rst
@@ -69,6 +69,11 @@ Bug Fixes
   for zarr writes. Existing zarr stores written with the old ``int8`` encoding
   are still read correctly. (:issue:`2937`, :pull:`11318`)
   By `Evan Lyall <https://github.com/elyall>`_.
+- No longer emit a ``SerializationWarning`` about a missing ``_FillValue`` when
+  encoding a CF coordinate variable (a 1D variable named after its dimension) to
+  an integer dtype. CF forbids missing values in coordinate variables, so a
+  ``_FillValue`` is not expected there (:issue:`10305`).
+  By `NoiceHax <https://github.com/NoiceHax>`_.
 - Raise an informative ``TypeError`` when a :py:class:`~xarray.Coordinates` object is
   passed as a coordinate value, e.g. ``ds.assign_coords({"x": coords})``, instead
   of silently creating a broken coordinate. Pass the object directly with
diff --git a/pyproject.toml b/pyproject.toml
index 6fad5adacff..e1b812bf087 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -425,6 +425,7 @@ Celles = "Celles"
 slowy = "slowy"
 Commun = "Commun"
 Noice = "Noice"
+Hax = "Hax"
 
 # Tests
 Ome = "Ome"
diff --git a/xarray/coding/variables.py b/xarray/coding/variables.py
index 6a5deb09152..42976533819 100644
--- a/xarray/coding/variables.py
+++ b/xarray/coding/variables.py
@@ -635,10 +635,14 @@ def encode(self, variable: Variable, name: T_Name = None) -> Variable:
             dtype = np.dtype(encoding.pop("dtype"))
             if dtype != variable.dtype:
                 if np.issubdtype(dtype, np.integer):
+                    # CF coordinate variables are not allowed to have missing values, so
+                    # they do not need a _FillValue. For simplicity we don't warn with 1D dimension coordinates.
+                    # http://cfconventions.org/cf-conventions/cf-conventions.html#missing-data
                     if (
                         np.issubdtype(variable.dtype, np.floating)
                         and "_FillValue" not in variable.attrs
                         and "missing_value" not in variable.attrs
+                        and dims != (name,)
                     ):
                         warnings.warn(
                             f"saving variable {name} with floating "
diff --git a/xarray/tests/test_conventions.py b/xarray/tests/test_conventions.py
index fd76aed836b..a0aac08c918 100644
--- a/xarray/tests/test_conventions.py
+++ b/xarray/tests/test_conventions.py
@@ -173,6 +173,27 @@ def test_missing_fillvalue(self) -> None:
             "invalid value encountered in cast" in msg for msg in warning_messages
         )
 
+    def test_missing_fillvalue_coordinate_variable(self) -> None:
+        # regression test for GH10305
+        # CF coordinate variables cannot have missing values, so they do not
+        # need a _FillValue and should not warn about one being absent
+        v = Variable(["x"], np.array([0.0, 1.0, 2.0]), encoding={"dtype": "int16"})
+        with warnings.catch_warnings():
+            warnings.simplefilter("error")
+            encoded = conventions.encode_cf_variable(v, name="x")
+        assert encoded.dtype == np.dtype("int16")
+
+    def test_missing_fillvalue_non_coordinate_variable(self) -> None:
+        # data variables and multidimensional (auxiliary) coordinates may hold
+        # missing values, so they still warn
+        v = Variable(["x"], np.array([0.0, 1.0, 2.0]), encoding={"dtype": "int16"})
+        with pytest.warns(SerializationWarning, match="floating point data"):
+            conventions.encode_cf_variable(v, name="data")
+
+        v2d = Variable(["y", "x"], np.zeros((2, 3)), encoding={"dtype": "int16"})
+        with pytest.warns(SerializationWarning, match="floating point data"):
+            conventions.encode_cf_variable(v2d, name="lat")
+
     def test_multidimensional_coordinates(self) -> None:
         # regression test for GH1763
         # Set up test case with coordinates that have overlapping (but not