diff --git a/xarray/core/combine.py b/xarray/core/combine.py
index 6f652cb6597..4b4a07ddc77 100644
--- a/xarray/core/combine.py
+++ b/xarray/core/combine.py
@@ -89,10 +89,12 @@ def _infer_concat_order_from_coords(datasets):
             # Need to read coordinate values to do ordering
             indexes = [ds._indexes.get(dim) for ds in datasets]
             if any(index is None for index in indexes):
-                raise ValueError(
-                    "Every dimension needs a coordinate for "
-                    "inferring concatenation order"
+                error_msg = (
+                    f"Every dimension requires a corresponding 1D coordinate "
+                    f"and index for inferring concatenation order but the "
+                    f"coordinate '{dim}' has no corresponding index"
                 )
+                raise ValueError(error_msg)
 
             # TODO (benbovy, flexible indexes): support flexible indexes?
             indexes = [index.to_pandas_index() for index in indexes]
diff --git a/xarray/tests/test_combine.py b/xarray/tests/test_combine.py
index aad7103c112..1c48dca825d 100644
--- a/xarray/tests/test_combine.py
+++ b/xarray/tests/test_combine.py
@@ -728,7 +728,10 @@ def test_combine_by_coords(self):
             combine_by_coords(objs)
 
         objs = [Dataset({"x": [0], "y": [0]}), Dataset({"x": [0]})]
-        with pytest.raises(ValueError, match=r"Every dimension needs a coordinate"):
+        with pytest.raises(
+            ValueError,
+            match=r"Every dimension requires a corresponding 1D coordinate and index",
+        ):
             combine_by_coords(objs)
 
     def test_empty_input(self):