diff --git a/doc/source/reference/indexing.rst b/doc/source/reference/indexing.rst
index 6e58f487d5f4a..1ce75f5aac877 100644
--- a/doc/source/reference/indexing.rst
+++ b/doc/source/reference/indexing.rst
@@ -407,6 +407,7 @@ Methods
     :toctree: api/
 
     DatetimeIndex.mean
+    DatetimeIndex.std
 
 TimedeltaIndex
 --------------
diff --git a/pandas/core/arrays/datetimes.py b/pandas/core/arrays/datetimes.py
index eb7638df301f7..71d38d3b3f73b 100644
--- a/pandas/core/arrays/datetimes.py
+++ b/pandas/core/arrays/datetimes.py
@@ -1923,6 +1923,26 @@ def std(
         keepdims: bool = False,
         skipna: bool = True,
     ):
+        """
+        Return sample standard deviation over requested axis.
+
+        Normalized by N-1 by default. This can be changed using the ddof argument
+
+        Parameters
+        ----------
+        axis : int optional, default None
+            Axis for the function to be applied on.
+        ddof : int, default 1
+            Degrees of Freedom. The divisor used in calculations is N - ddof,
+            where N represents the number of elements.
+        skipna : bool, default True
+            Exclude NA/null values. If an entire row/column is NA, the result will be
+            NA.
+
+        Returns
+        -------
+        Timedelta
+        """
         # Because std is translation-invariant, we can get self.std
         #  by calculating (self - Timestamp(0)).std, and we can do it
         #  without creating a copy by using a view on self._ndarray