diff --git a/doc/source/whatsnew/v2.1.0.rst b/doc/source/whatsnew/v2.1.0.rst
index 410a324be829e..dfa5adaaeadee 100644
--- a/doc/source/whatsnew/v2.1.0.rst
+++ b/doc/source/whatsnew/v2.1.0.rst
@@ -208,6 +208,7 @@ Groupby/resample/rolling
 Reshaping
 ^^^^^^^^^
 - Bug in :meth:`DataFrame.stack` losing extension dtypes when columns is a :class:`MultiIndex` and frame contains mixed dtypes (:issue:`45740`)
+- Bug in :func:`concat` sorting :class:`Index` when all passed objects have :class:`DatetimeIndex` indexes (:issue:`51210`)
 - Bug in :meth:`DataFrame.transpose` inferring dtype for object column (:issue:`51546`)
 - Bug in :meth:`Series.combine_first` converting ``int64`` dtype to ``float64`` and losing precision on very large integers (:issue:`51764`)
 -
diff --git a/pandas/core/indexes/api.py b/pandas/core/indexes/api.py
index f880e1f10106d..01648c271cef8 100644
--- a/pandas/core/indexes/api.py
+++ b/pandas/core/indexes/api.py
@@ -280,7 +280,6 @@ def _find_common_index_dtype(inds):
             raise TypeError("Cannot join tz-naive with tz-aware DatetimeIndex")
 
         if len(dtis) == len(indexes):
-            sort = True
             result = indexes[0]
 
         elif len(dtis) > 1:
diff --git a/pandas/tests/reshape/concat/test_datetimes.py b/pandas/tests/reshape/concat/test_datetimes.py
index 43c6bb03b6a9a..b3555e7928415 100644
--- a/pandas/tests/reshape/concat/test_datetimes.py
+++ b/pandas/tests/reshape/concat/test_datetimes.py
@@ -77,23 +77,23 @@ def test_concat_datetime_timezone(self):
 
         exp_idx = DatetimeIndex(
             [
-                "2010-12-31 15:00:00+00:00",
-                "2010-12-31 16:00:00+00:00",
-                "2010-12-31 17:00:00+00:00",
                 "2010-12-31 23:00:00+00:00",
                 "2011-01-01 00:00:00+00:00",
                 "2011-01-01 01:00:00+00:00",
+                "2010-12-31 15:00:00+00:00",
+                "2010-12-31 16:00:00+00:00",
+                "2010-12-31 17:00:00+00:00",
             ]
         )
 
         expected = DataFrame(
             [
-                [np.nan, 1],
-                [np.nan, 2],
-                [np.nan, 3],
                 [1, np.nan],
                 [2, np.nan],
                 [3, np.nan],
+                [np.nan, 1],
+                [np.nan, 2],
+                [np.nan, 3],
             ],
             index=exp_idx,
             columns=["a", "b"],