diff --git a/pandas/core/algorithms.py b/pandas/core/algorithms.py
index 932ac71a23ed0..bdb73fa246d4f 100644
--- a/pandas/core/algorithms.py
+++ b/pandas/core/algorithms.py
@@ -16,12 +16,12 @@
 from pandas.core.dtypes.common import (
     ensure_float64, ensure_int64, ensure_object, ensure_platform_int,
     ensure_uint64, is_array_like, is_bool_dtype, is_categorical_dtype,
-    is_complex_dtype, is_datetime64_any_dtype, is_datetime64tz_dtype,
-    is_datetimelike, is_extension_array_dtype, is_float_dtype, is_integer,
-    is_integer_dtype, is_interval_dtype, is_list_like, is_numeric_dtype,
-    is_object_dtype, is_period_dtype, is_scalar, is_signed_integer_dtype,
-    is_sparse, is_timedelta64_dtype, is_unsigned_integer_dtype,
-    needs_i8_conversion)
+    is_complex_dtype, is_datetime64_any_dtype, is_datetime64_ns_dtype,
+    is_datetime64tz_dtype, is_datetimelike, is_extension_array_dtype,
+    is_float_dtype, is_integer, is_integer_dtype, is_interval_dtype,
+    is_list_like, is_numeric_dtype, is_object_dtype, is_period_dtype,
+    is_scalar, is_signed_integer_dtype, is_sparse, is_timedelta64_dtype,
+    is_unsigned_integer_dtype, needs_i8_conversion)
 from pandas.core.dtypes.generic import ABCIndex, ABCIndexClass, ABCSeries
 from pandas.core.dtypes.missing import isna, na_value_for_dtype
 
@@ -104,6 +104,13 @@ def _ensure_data(values, dtype=None):
             dtype = values.dtype
         else:
             # Datetime
+            if values.ndim > 1 and is_datetime64_ns_dtype(values):
+                # Avoid calling the DatetimeIndex constructor as it is 1D only
+                # Note: this is reached by DataFrame.rank calls GH#27027
+                asi8 = values.view('i8')
+                dtype = values.dtype
+                return asi8, dtype, 'int64'
+
             from pandas import DatetimeIndex
             values = DatetimeIndex(values)
             dtype = values.dtype
diff --git a/pandas/core/arrays/datetimes.py b/pandas/core/arrays/datetimes.py
index 6e7217762a3fb..eaa0278da6dc3 100644
--- a/pandas/core/arrays/datetimes.py
+++ b/pandas/core/arrays/datetimes.py
@@ -309,6 +309,8 @@ def __init__(self, values, dtype=_NS_DTYPE, freq=None, copy=False):
                 "ndarray, or Series or Index containing one of those."
             )
             raise ValueError(msg.format(type(values).__name__))
+        if values.ndim != 1:
+            raise ValueError("Only 1-dimensional input arrays are supported.")
 
         if values.dtype == 'i8':
             # for compat with datetime/timedelta/period shared methods,
diff --git a/pandas/io/formats/format.py b/pandas/io/formats/format.py
index b2ef45b15e549..1efcb63269454 100644
--- a/pandas/io/formats/format.py
+++ b/pandas/io/formats/format.py
@@ -1273,6 +1273,8 @@ def format_percentiles(percentiles):
 
 def _is_dates_only(values):
     # return a boolean if we are only dates (and don't have a timezone)
+    assert values.ndim == 1
+
     values = DatetimeIndex(values)
     if values.tz is not None:
         return False
@@ -1324,6 +1326,12 @@ def _get_format_datetime64(is_dates_only, nat_rep='NaT', date_format=None):
 
 def _get_format_datetime64_from_values(values, date_format):
     """ given values and a date_format, return a string format """
+
+    if isinstance(values, np.ndarray) and values.ndim > 1:
+        # We don't actaully care about the order of values, and DatetimeIndex
+        #  only accepts 1D values
+        values = values.ravel()
+
     is_dates_only = _is_dates_only(values)
     if is_dates_only:
         return date_format or "%Y-%m-%d"
diff --git a/pandas/tests/arrays/test_datetimes.py b/pandas/tests/arrays/test_datetimes.py
index 1218527f6fd9b..c7c0e1180ce46 100644
--- a/pandas/tests/arrays/test_datetimes.py
+++ b/pandas/tests/arrays/test_datetimes.py
@@ -15,6 +15,18 @@
 
 
 class TestDatetimeArrayConstructor:
+
+    def test_only_1dim_accepted(self):
+        arr = np.array([0, 1, 2, 3], dtype='M8[h]').astype('M8[ns]')
+
+        with pytest.raises(ValueError, match="Only 1-dimensional"):
+            # 2-dim
+            DatetimeArray(arr.reshape(2, 2))
+
+        with pytest.raises(ValueError, match="Only 1-dimensional"):
+            # 0-dim
+            DatetimeArray(arr[[0]].squeeze())
+
     def test_freq_validation(self):
         # GH#24623 check that invalid instances cannot be created with the
         #  public constructor