diff --git a/doc/whats-new.rst b/doc/whats-new.rst
index 0b611e88453..6b944fd1b30 100644
--- a/doc/whats-new.rst
+++ b/doc/whats-new.rst
@@ -39,7 +39,10 @@ Bug fixes
 - Fix silently overwriting the `engine` key when passing :py:func:`open_dataset` a file object
   to an incompatible netCDF (:issue:`4457`). Now incompatible combinations of files and engines raise
   an exception instead. By `Alessandro Amici <https://github.com/alexamici>`_.
-
+- The ``min_count`` argument to :py:meth:`DataArray.sum()` and :py:meth:`DataArray.prod()`
+  is now ignored when not applicable, i.e. when ``skipna=False`` or when ``skipna=None``
+  and the dtype does not have a missing value (:issue:`4352`).
+  By `Mathias Hauser <https://github.com/mathause>`_.
 
 Documentation
 ~~~~~~~~~~~~~
diff --git a/xarray/core/duck_array_ops.py b/xarray/core/duck_array_ops.py
index 53849a3eac8..f35dfd236be 100644
--- a/xarray/core/duck_array_ops.py
+++ b/xarray/core/duck_array_ops.py
@@ -325,6 +325,8 @@ def f(values, axis=None, skipna=None, **kwargs):
             nanname = "nan" + name
             func = getattr(nanops, nanname)
         else:
+            if name in ["sum", "prod"]:
+                kwargs.pop("min_count", None)
             func = _dask_or_eager_func(name, dask_module=dask_module)
 
         try:
@@ -361,7 +363,7 @@ def f(values, axis=None, skipna=None, **kwargs):
 median.numeric_only = True
 prod = _create_nan_agg_method("prod")
 prod.numeric_only = True
-sum.available_min_count = True
+prod.available_min_count = True
 cumprod_1d = _create_nan_agg_method("cumprod")
 cumprod_1d.numeric_only = True
 cumsum_1d = _create_nan_agg_method("cumsum")
diff --git a/xarray/tests/test_duck_array_ops.py b/xarray/tests/test_duck_array_ops.py
index 41f03115bc3..44b2ed23357 100644
--- a/xarray/tests/test_duck_array_ops.py
+++ b/xarray/tests/test_duck_array_ops.py
@@ -580,15 +580,17 @@ def test_dask_gradient(axis, edge_order):
 @pytest.mark.parametrize("dask", [False, True])
 @pytest.mark.parametrize("func", ["sum", "prod"])
 @pytest.mark.parametrize("aggdim", [None, "x"])
-def test_min_count(dim_num, dtype, dask, func, aggdim):
+@pytest.mark.parametrize("contains_nan", [True, False])
+@pytest.mark.parametrize("skipna", [True, False, None])
+def test_min_count(dim_num, dtype, dask, func, aggdim, contains_nan, skipna):
     if dask and not has_dask:
         pytest.skip("requires dask")
 
-    da = construct_dataarray(dim_num, dtype, contains_nan=True, dask=dask)
+    da = construct_dataarray(dim_num, dtype, contains_nan=contains_nan, dask=dask)
     min_count = 3
 
-    actual = getattr(da, func)(dim=aggdim, skipna=True, min_count=min_count)
-    expected = series_reduce(da, func, skipna=True, dim=aggdim, min_count=min_count)
+    actual = getattr(da, func)(dim=aggdim, skipna=skipna, min_count=min_count)
+    expected = series_reduce(da, func, skipna=skipna, dim=aggdim, min_count=min_count)
     assert_allclose(actual, expected)
     assert_dask_array(actual, dask)