diff --git a/doc/whats-new.rst b/doc/whats-new.rst
index 75a273bfdb4..57d29292f72 100644
--- a/doc/whats-new.rst
+++ b/doc/whats-new.rst
@@ -135,6 +135,8 @@ Bug fixes
 - Fix error that arises when using open_mfdataset on a series of netcdf files
   having differing values for a variable attribute of type list. (:issue:`3034`)
   By `Hasan Ahmad <https://github.com/HasanAhmadQ7>`_.
+- Prevent :py:meth:`~xarray.DataArray.argmax` and :py:meth:`~xarray.DataArray.argmin` from calling
+  dask compute (:issue:`3237`). By `Ulrich Herter <https://github.com/ulijh>`_.
 
 .. _whats-new.0.12.3:
 
diff --git a/xarray/core/nanops.py b/xarray/core/nanops.py
index 9ba4eae29ae..17240faf007 100644
--- a/xarray/core/nanops.py
+++ b/xarray/core/nanops.py
@@ -88,38 +88,21 @@ def nanmax(a, axis=None, out=None):
 
 
 def nanargmin(a, axis=None):
-    fill_value = dtypes.get_pos_infinity(a.dtype)
     if a.dtype.kind == "O":
+        fill_value = dtypes.get_pos_infinity(a.dtype)
         return _nan_argminmax_object("argmin", fill_value, a, axis=axis)
-    a, mask = _replace_nan(a, fill_value)
-    if isinstance(a, dask_array_type):
-        res = dask_array.argmin(a, axis=axis)
-    else:
-        res = np.argmin(a, axis=axis)
 
-    if mask is not None:
-        mask = mask.all(axis=axis)
-        if mask.any():
-            raise ValueError("All-NaN slice encountered")
-    return res
+    module = dask_array if isinstance(a, dask_array_type) else nputils
+    return module.nanargmin(a, axis=axis)
 
 
 def nanargmax(a, axis=None):
-    fill_value = dtypes.get_neg_infinity(a.dtype)
     if a.dtype.kind == "O":
+        fill_value = dtypes.get_neg_infinity(a.dtype)
         return _nan_argminmax_object("argmax", fill_value, a, axis=axis)
 
-    a, mask = _replace_nan(a, fill_value)
-    if isinstance(a, dask_array_type):
-        res = dask_array.argmax(a, axis=axis)
-    else:
-        res = np.argmax(a, axis=axis)
-
-    if mask is not None:
-        mask = mask.all(axis=axis)
-        if mask.any():
-            raise ValueError("All-NaN slice encountered")
-    return res
+    module = dask_array if isinstance(a, dask_array_type) else nputils
+    return module.nanargmax(a, axis=axis)
 
 
 def nansum(a, axis=None, dtype=None, out=None, min_count=None):
diff --git a/xarray/core/nputils.py b/xarray/core/nputils.py
index 769af03fe6a..df36c98f94c 100644
--- a/xarray/core/nputils.py
+++ b/xarray/core/nputils.py
@@ -237,3 +237,5 @@ def f(values, axis=None, **kwargs):
 nanprod = _create_bottleneck_method("nanprod")
 nancumsum = _create_bottleneck_method("nancumsum")
 nancumprod = _create_bottleneck_method("nancumprod")
+nanargmin = _create_bottleneck_method("nanargmin")
+nanargmax = _create_bottleneck_method("nanargmax")
diff --git a/xarray/tests/test_dask.py b/xarray/tests/test_dask.py
index e3fc6f65e0f..d105765481e 100644
--- a/xarray/tests/test_dask.py
+++ b/xarray/tests/test_dask.py
@@ -27,14 +27,49 @@
 dd = pytest.importorskip("dask.dataframe")
 
 
+class CountingScheduler:
+    """ Simple dask scheduler counting the number of computes.
+
+    Reference: https://stackoverflow.com/questions/53289286/ """
+
+    def __init__(self, max_computes=0):
+        self.total_computes = 0
+        self.max_computes = max_computes
+
+    def __call__(self, dsk, keys, **kwargs):
+        self.total_computes += 1
+        if self.total_computes > self.max_computes:
+            raise RuntimeError(
+                "Too many computes. Total: %d > max: %d."
+                % (self.total_computes, self.max_computes)
+            )
+        return dask.get(dsk, keys, **kwargs)
+
+
+def _set_dask_scheduler(scheduler=dask.get):
+    """ Backwards compatible way of setting scheduler. """
+    if LooseVersion(dask.__version__) >= LooseVersion("0.18.0"):
+        return dask.config.set(scheduler=scheduler)
+    return dask.set_options(get=scheduler)
+
+
+def raise_if_dask_computes(max_computes=0):
+    scheduler = CountingScheduler(max_computes)
+    return _set_dask_scheduler(scheduler)
+
+
+def test_raise_if_dask_computes():
+    data = da.from_array(np.random.RandomState(0).randn(4, 6), chunks=(2, 2))
+    with raises_regex(RuntimeError, "Too many computes"):
+        with raise_if_dask_computes():
+            data.compute()
+
+
 class DaskTestCase:
     def assertLazyAnd(self, expected, actual, test):
-
-        with (
-            dask.config.set(scheduler="single-threaded")
-            if LooseVersion(dask.__version__) >= LooseVersion("0.18.0")
-            else dask.set_options(get=dask.get)
-        ):
+        with _set_dask_scheduler(dask.get):
+            # dask.get is the syncronous scheduler, which get's set also by
+            # dask.config.set(scheduler="syncronous") in current versions.
             test(actual, expected)
 
         if isinstance(actual, Dataset):
@@ -174,7 +209,12 @@ def test_reduce(self):
         v = self.lazy_var
         self.assertLazyAndAllClose(u.mean(), v.mean())
         self.assertLazyAndAllClose(u.std(), v.std())
-        self.assertLazyAndAllClose(u.argmax(dim="x"), v.argmax(dim="x"))
+        with raise_if_dask_computes():
+            actual = v.argmax(dim="x")
+        self.assertLazyAndAllClose(u.argmax(dim="x"), actual)
+        with raise_if_dask_computes():
+            actual = v.argmin(dim="x")
+        self.assertLazyAndAllClose(u.argmin(dim="x"), actual)
         self.assertLazyAndAllClose((u > 1).any(), (v > 1).any())
         self.assertLazyAndAllClose((u < 1).all("x"), (v < 1).all("x"))
         with raises_regex(NotImplementedError, "dask"):