diff --git a/doc/whats-new.rst b/doc/whats-new.rst
index 753586c32c2..8c6b3a099c2 100644
--- a/doc/whats-new.rst
+++ b/doc/whats-new.rst
@@ -49,6 +49,9 @@ Bug fixes
   By `Michael Niklas <https://github.com/headtr1ck>`_.
 - Dark themes are now properly detected for ``html[data-theme=dark]``-tags (:pull:`9200`).
   By `Dieter Werthmüller <https://github.com/prisae>`_.
+- Reductions no longer fail for ``np.complex_`` dtype arrays when numbagg is
+  installed.
+  By `Maximilian Roos <https://github.com/max-sixty>`_
 
 Documentation
 ~~~~~~~~~~~~~
diff --git a/xarray/core/nputils.py b/xarray/core/nputils.py
index 6970d37402f..1d30fe9db9e 100644
--- a/xarray/core/nputils.py
+++ b/xarray/core/nputils.py
@@ -191,7 +191,7 @@ def f(values, axis=None, **kwargs):
                 or kwargs.get("ddof", 0) == 1
             )
             # TODO: bool?
-            and values.dtype.kind in "uifc"
+            and values.dtype.kind in "uif"
             # and values.dtype.isnative
             and (dtype is None or np.dtype(dtype) == values.dtype)
             # numbagg.nanquantile only available after 0.8.0 and with linear method
diff --git a/xarray/tests/test_computation.py b/xarray/tests/test_computation.py
index 080447cede0..4b9b95b27bb 100644
--- a/xarray/tests/test_computation.py
+++ b/xarray/tests/test_computation.py
@@ -2598,3 +2598,11 @@ def test_cross(a, b, ae, be, dim: str, axis: int, use_dask: bool) -> None:
 
     actual = xr.cross(a, b, dim=dim)
     xr.testing.assert_duckarray_allclose(expected, actual)
+
+
+@pytest.mark.parametrize("compute_backend", ["numbagg"], indirect=True)
+def test_complex_number_reduce(compute_backend):
+    da = xr.DataArray(np.ones((2,), dtype=np.complex_), dims=["x"])
+    # Check that xarray doesn't call into numbagg, which doesn't compile for complex
+    # numbers at the moment (but will when numba supports dynamic compilation)
+    da.min()