diff --git a/doc/whats-new.rst b/doc/whats-new.rst
index db8c43d3726..6bfdf0b6f0a 100644
--- a/doc/whats-new.rst
+++ b/doc/whats-new.rst
@@ -35,6 +35,8 @@ Deprecations
 Bug fixes
 ~~~~~~~~~
 
+- Fix :py:meth:`xr.polyval` with non-system standard integer coeffs (:pull:`7619`).
+  By `Shreyal Gupta <https://github.com/Ravenin7>`_ and `Michael Niklas <https://github.com/headtr1ck>`_.
 
 Documentation
 ~~~~~~~~~~~~~
diff --git a/xarray/core/computation.py b/xarray/core/computation.py
index 2305e753cee..9b282d32a45 100644
--- a/xarray/core/computation.py
+++ b/xarray/core/computation.py
@@ -1968,7 +1968,7 @@ def polyval(
         raise ValueError(
             f"Dimension `{degree_dim}` should be a coordinate variable with labels."
         )
-    if not np.issubdtype(coeffs[degree_dim].dtype, int):
+    if not np.issubdtype(coeffs[degree_dim].dtype, np.integer):
         raise ValueError(
             f"Dimension `{degree_dim}` should be of integer dtype. Received {coeffs[degree_dim].dtype} instead."
         )
diff --git a/xarray/tests/test_computation.py b/xarray/tests/test_computation.py
index 8e45a07d6a2..3c10e3f27ab 100644
--- a/xarray/tests/test_computation.py
+++ b/xarray/tests/test_computation.py
@@ -2092,6 +2092,36 @@ def test_where_attrs() -> None:
             xr.DataArray([1000.0, 2000.0, 3000.0], dims="x"),
             id="timedelta",
         ),
+        pytest.param(
+            xr.DataArray([1, 2, 3], dims="x"),
+            xr.DataArray(
+                [2, 3, 4],
+                dims="degree",
+                coords={"degree": np.array([0, 1, 2], dtype=np.int64)},
+            ),
+            xr.DataArray([9, 2 + 6 + 16, 2 + 9 + 36], dims="x"),
+            id="int64-degree",
+        ),
+        pytest.param(
+            xr.DataArray([1, 2, 3], dims="x"),
+            xr.DataArray(
+                [2, 3, 4],
+                dims="degree",
+                coords={"degree": np.array([0, 1, 2], dtype=np.int32)},
+            ),
+            xr.DataArray([9, 2 + 6 + 16, 2 + 9 + 36], dims="x"),
+            id="int32-degree",
+        ),
+        pytest.param(
+            xr.DataArray([1, 2, 3], dims="x"),
+            xr.DataArray(
+                [2, 3, 4],
+                dims="degree",
+                coords={"degree": np.array([0, 1, 2], dtype=np.uint8)},
+            ),
+            xr.DataArray([9, 2 + 6 + 16, 2 + 9 + 36], dims="x"),
+            id="uint8-degree",
+        ),
     ],
 )
 def test_polyval(