diff --git a/xarray/core/indexes.py b/xarray/core/indexes.py
index 9223631915f..f1cc7dfaed1 100644
--- a/xarray/core/indexes.py
+++ b/xarray/core/indexes.py
@@ -129,6 +129,15 @@ def _is_nested_tuple(possible_tuple):
     )
 
 
+def normalize_label(value, extract_scalar=False):
+    if getattr(value, "ndim", 1) <= 1:
+        value = _asarray_tuplesafe(value)
+    if extract_scalar:
+        # see https://github.com/pydata/xarray/pull/4292 for details
+        value = value[()] if value.dtype.kind in "mM" else value.item()
+    return value
+
+
 def get_indexer_nd(index, labels, method=None, tolerance=None):
     """Wrapper around :meth:`pandas.Index.get_indexer` supporting n-dimensional
     labels
@@ -207,14 +216,9 @@ def query(self, labels, method=None, tolerance=None):
                 "a dimension that does not have a MultiIndex"
             )
         else:
-            label = (
-                label
-                if getattr(label, "ndim", 1) > 1  # vectorized-indexing
-                else _asarray_tuplesafe(label)
-            )
+            label = normalize_label(label)
             if label.ndim == 0:
-                # see https://github.com/pydata/xarray/pull/4292 for details
-                label_value = label[()] if label.dtype.kind in "mM" else label.item()
+                label_value = normalize_label(label, extract_scalar=True)
                 if isinstance(self.index, pd.CategoricalIndex):
                     if method is not None:
                         raise ValueError(
@@ -336,6 +340,10 @@ def query(self, labels, method=None, tolerance=None):
         # label(s) given for multi-index level(s)
         if all([lbl in self.index.names for lbl in labels]):
             is_nested_vals = _is_nested_tuple(tuple(labels.values()))
+            labels = {
+                k: normalize_label(v, extract_scalar=True) for k, v in labels.items()
+            }
+
             if len(labels) == self.index.nlevels and not is_nested_vals:
                 indexer = self.index.get_loc(tuple(labels[k] for k in self.index.names))
             else:
diff --git a/xarray/tests/test_dataarray.py b/xarray/tests/test_dataarray.py
index 8ab8bc872da..5205c1b59ab 100644
--- a/xarray/tests/test_dataarray.py
+++ b/xarray/tests/test_dataarray.py
@@ -1006,6 +1006,20 @@ def test_sel_float(self):
         assert_equal(expected_scalar, actual_scalar)
         assert_equal(expected_16, actual_16)
 
+    def test_sel_float_multiindex(self):
+        # regression test https://github.com/pydata/xarray/issues/5691
+        midx = pd.MultiIndex.from_arrays(
+            [["a", "a", "b", "b"], [0.1, 0.2, 0.3, 0.4]], names=["lvl1", "lvl2"]
+        )
+        da = xr.DataArray([1, 2, 3, 4], coords={"x": midx}, dims="x")
+
+        actual = da.sel(lvl1="a", lvl2=0.1)
+        expected = da.isel(x=0)
+
+        assert_equal(actual, expected)
+
+        # TODO: test multi-index created from coordinates, one with dtype=float32
+
     def test_sel_no_index(self):
         array = DataArray(np.arange(10), dims="x")
         assert_identical(array[0], array.sel(x=0))