diff --git a/doc/source/whatsnew/v3.0.0.rst b/doc/source/whatsnew/v3.0.0.rst
index 2b35abd45a96f..38755aef32b85 100644
--- a/doc/source/whatsnew/v3.0.0.rst
+++ b/doc/source/whatsnew/v3.0.0.rst
@@ -999,6 +999,7 @@ Datetimelike
 - Bug in comparison between objects with pyarrow date dtype and ``timestamp[pyarrow]`` or ``np.datetime64`` dtype failing to consider these as non-comparable (:issue:`62157`)
 - Bug in constructing arrays with :class:`ArrowDtype` with ``timestamp`` type incorrectly allowing ``Decimal("NaN")`` (:issue:`61773`)
 - Bug in constructing arrays with a timezone-aware :class:`ArrowDtype` from timezone-naive datetime objects incorrectly treating those as UTC times instead of wall times like :class:`DatetimeTZDtype` (:issue:`61775`)
+- Bug in retaining frequency in :meth:`value_counts` specifically for :meth:`DatetimeIndex` and :meth:`TimedeltaIndex` (:issue:`33830`)
 - Bug in setting scalar values with mismatched resolution into arrays with non-nanosecond ``datetime64``, ``timedelta64`` or :class:`DatetimeTZDtype` incorrectly truncating those scalars (:issue:`56410`)
 
 Timedelta
diff --git a/pandas/core/algorithms.py b/pandas/core/algorithms.py
index 03127e58a9f41..b977e998b82a4 100644
--- a/pandas/core/algorithms.py
+++ b/pandas/core/algorithms.py
@@ -868,8 +868,10 @@ def value_counts_internal(
     dropna: bool = True,
 ) -> Series:
     from pandas import (
+        DatetimeIndex,
         Index,
         Series,
+        TimedeltaIndex,
     )
 
     index_name = getattr(values, "name", None)
@@ -934,6 +936,17 @@ def value_counts_internal(
             # Starting in 3.0, we no longer perform dtype inference on the
             #  Index object we construct here, xref GH#56161
             idx = Index(keys, dtype=keys.dtype, name=index_name)
+
+            if (
+                bins is None
+                and not sort
+                and isinstance(values, (DatetimeIndex, TimedeltaIndex))
+                and idx.equals(values)
+                and values.inferred_freq is not None
+            ):
+                # Preserve freq of original index
+                idx.freq = values.inferred_freq  # type: ignore[attr-defined]
+
             result = Series(counts, index=idx, name=name, copy=False)
 
     if sort:
diff --git a/pandas/tests/base/test_value_counts.py b/pandas/tests/base/test_value_counts.py
index bcb31829a201f..f642d26c32f5d 100644
--- a/pandas/tests/base/test_value_counts.py
+++ b/pandas/tests/base/test_value_counts.py
@@ -14,6 +14,7 @@
     Series,
     Timedelta,
     TimedeltaIndex,
+    Timestamp,
     array,
 )
 import pandas._testing as tm
@@ -339,3 +340,81 @@ def test_value_counts_object_inference_deprecated():
     exp = dti.value_counts()
     exp.index = exp.index.astype(object)
     tm.assert_series_equal(res, exp)
+
+
+@pytest.mark.parametrize(
+    ("index", "expected_index"),
+    [
+        [
+            pd.date_range("2016-01-01", periods=5, freq="D"),
+            pd.date_range("2016-01-01", periods=5, freq="D"),
+        ],
+        [
+            pd.timedelta_range(Timedelta(0), periods=5, freq="h"),
+            pd.timedelta_range(Timedelta(0), periods=5, freq="h"),
+        ],
+        [
+            DatetimeIndex(
+                [Timestamp("2016-01-01") + Timedelta(days=i) for i in range(1)]
+                + [Timestamp("2016-01-02")]
+                + [Timestamp("2016-01-01") + Timedelta(days=i) for i in range(1, 5)]
+            ),
+            DatetimeIndex(pd.date_range("2016-01-01", periods=5, freq="D")),
+        ],
+        [
+            TimedeltaIndex(
+                [Timedelta(hours=i) for i in range(1)]
+                + [Timedelta(hours=1)]
+                + [Timedelta(hours=i) for i in range(1, 5)],
+            ),
+            TimedeltaIndex(pd.timedelta_range(Timedelta(0), periods=5, freq="h")),
+        ],
+        [
+            DatetimeIndex(
+                [Timestamp("2016-01-01") + Timedelta(days=i) for i in range(2)]
+                + [Timestamp("2016-01-01") + Timedelta(days=i) for i in range(3, 5)],
+            ),
+            DatetimeIndex(
+                [Timestamp("2016-01-01") + Timedelta(days=i) for i in range(2)]
+                + [Timestamp("2016-01-01") + Timedelta(days=i) for i in range(3, 5)],
+            ),
+        ],
+        [
+            TimedeltaIndex(
+                [Timedelta(hours=i) for i in range(2)]
+                + [Timedelta(hours=i) for i in range(3, 5)],
+            ),
+            TimedeltaIndex(
+                [Timedelta(hours=i) for i in range(2)]
+                + [Timedelta(hours=i) for i in range(3, 5)],
+            ),
+        ],
+        [
+            DatetimeIndex(
+                [Timestamp("2016-01-01")]
+                + [pd.NaT]
+                + [Timestamp("2016-01-01") + Timedelta(days=i) for i in range(1, 5)],
+            ),
+            DatetimeIndex(
+                [Timestamp("2016-01-01")]
+                + [pd.NaT]
+                + [Timestamp("2016-01-01") + Timedelta(days=i) for i in range(1, 5)],
+            ),
+        ],
+        [
+            TimedeltaIndex(
+                [Timedelta(hours=0)]
+                + [pd.NaT]
+                + [Timedelta(hours=i) for i in range(1, 5)],
+            ),
+            TimedeltaIndex(
+                [Timedelta(hours=0)]
+                + [pd.NaT]
+                + [Timedelta(hours=i) for i in range(1, 5)],
+            ),
+        ],
+    ],
+)
+def test_value_counts_index_datetimelike(index, expected_index):
+    vc = index.value_counts(sort=False, dropna=False)
+    tm.assert_index_equal(vc.index, expected_index)