diff --git a/doc/whats-new.rst b/doc/whats-new.rst
index f41e57989be..379c2c9d947 100644
--- a/doc/whats-new.rst
+++ b/doc/whats-new.rst
@@ -53,6 +53,10 @@ Bug fixes
 - Fix applying function with non-xarray arguments using :py:func:`xr.map_blocks`.
   By `Cindy Chiao <https://github.com/tcchiao>`_.
 
+- `dt.season <https://xarray.pydata.org/en/stable/generated/xarray.DataArray.dt.season.html>`_  can now handle NaN and NaT.  (:pull:`5876`).
+  By `Pierre Loicq <https://github.com/pierreloicq>`_.
+
+
 Documentation
 ~~~~~~~~~~~~~
 
diff --git a/xarray/core/accessor_dt.py b/xarray/core/accessor_dt.py
index 2a7b6200d3b..7f8bf79a50a 100644
--- a/xarray/core/accessor_dt.py
+++ b/xarray/core/accessor_dt.py
@@ -16,9 +16,20 @@
 def _season_from_months(months):
     """Compute season (DJF, MAM, JJA, SON) from month ordinal"""
     # TODO: Move "season" accessor upstream into pandas
-    seasons = np.array(["DJF", "MAM", "JJA", "SON"])
+    seasons = np.array(["DJF", "MAM", "JJA", "SON", "nan"])
     months = np.asarray(months)
-    return seasons[(months // 3) % 4]
+
+    with warnings.catch_warnings():
+        warnings.filterwarnings(
+            "ignore", message="invalid value encountered in floor_divide"
+        )
+        warnings.filterwarnings(
+            "ignore", message="invalid value encountered in remainder"
+        )
+        idx = (months // 3) % 4
+
+    idx[np.isnan(idx)] = 4
+    return seasons[idx.astype(int)]
 
 
 def _access_through_cftimeindex(values, name):
diff --git a/xarray/tests/test_accessor_dt.py b/xarray/tests/test_accessor_dt.py
index b471bd2e267..e9278f1e918 100644
--- a/xarray/tests/test_accessor_dt.py
+++ b/xarray/tests/test_accessor_dt.py
@@ -222,6 +222,7 @@ def test_dask_accessor_method(self, method, parameters) -> None:
 
     def test_seasons(self) -> None:
         dates = pd.date_range(start="2000/01/01", freq="M", periods=12)
+        dates = dates.append(pd.Index([np.datetime64("NaT")]))
         dates = xr.DataArray(dates)
         seasons = xr.DataArray(
             [
@@ -237,6 +238,7 @@ def test_seasons(self) -> None:
                 "SON",
                 "SON",
                 "DJF",
+                "nan",
             ]
         )