diff --git a/doc/whats-new.rst b/doc/whats-new.rst
index 373cb8d13dc..d7a9554fd40 100644
--- a/doc/whats-new.rst
+++ b/doc/whats-new.rst
@@ -77,6 +77,8 @@ Bug fixes
   By `Mayeul d'Avezac <https://github.com/mdavezac>`_.
 - Return correct count for scalar datetime64 arrays (:issue:`2770`)
   By `Dan Nowacki <https://github.com/dnowacki-usgs>`_.
+- Fixed max, min exception when applied to a multiIndex (:issue:`2923`)
+  By `Ian Castleden <https://github.com/arabidopsis>`_
 - A deep copy deep-copies the coords (:issue:`1463`)
   By `Martin Pletcher <https://github.com/pletchm>`_.
 - Increased support for `missing_value` (:issue:`2871`)
diff --git a/xarray/core/nanops.py b/xarray/core/nanops.py
index babc1dd97e6..06ab08e12fb 100644
--- a/xarray/core/nanops.py
+++ b/xarray/core/nanops.py
@@ -1,6 +1,6 @@
 import numpy as np
 
-from . import dtypes, nputils
+from . import dtypes, nputils, utils
 from .duck_array_ops import (
     _dask_or_eager_func, count, fillna, isnull, where_method)
 from .pycompat import dask_array_type
@@ -64,8 +64,10 @@ def _nan_minmax_object(func, fill_value, value, axis=None, **kwargs):
     filled_value = fillna(value, fill_value)
     data = getattr(np, func)(filled_value, axis=axis, **kwargs)
     if not hasattr(data, 'dtype'):  # scalar case
-        data = dtypes.fill_value(value.dtype) if valid_count == 0 else data
-        return np.array(data, dtype=value.dtype)
+        data = fill_value if valid_count == 0 else data
+        # we've computed a single min, max value of type object.
+        # don't let np.array turn a tuple back into an array
+        return utils.to_0d_object_array(data)
     return where_method(data, valid_count != 0)
 
 
diff --git a/xarray/tests/test_indexing.py b/xarray/tests/test_indexing.py
index 59435fea88b..c044d2ed1f3 100644
--- a/xarray/tests/test_indexing.py
+++ b/xarray/tests/test_indexing.py
@@ -43,6 +43,22 @@ def test_asarray_tuplesafe(self):
         assert res[0] == (0,)
         assert res[1] == (1,)
 
+    def test_stacked_multiindex_min_max(self):
+        data = np.random.randn(3, 23, 4)
+        da = DataArray(
+            data, name="value",
+            dims=["replicate", "rsample", "exp"],
+            coords=dict(
+                replicate=[0, 1, 2],
+                exp=["a", "b", "c", "d"],
+                rsample=list(range(23))
+            ),
+        )
+        da2 = da.stack(sample=("replicate", "rsample"))
+        s = da2.sample
+        assert_array_equal(da2.loc['a', s.max()], data[2, 22, 0])
+        assert_array_equal(da2.loc['b', s.min()], data[0, 0, 1])
+
     def test_convert_label_indexer(self):
         # TODO: add tests that aren't just for edge cases
         index = pd.Index([1, 2, 3])