diff --git a/doc/source/whatsnew/v3.0.0.rst b/doc/source/whatsnew/v3.0.0.rst
index c41524619de95..0796c58cd9dfc 100644
--- a/doc/source/whatsnew/v3.0.0.rst
+++ b/doc/source/whatsnew/v3.0.0.rst
@@ -976,6 +976,7 @@ 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`)
 
 
diff --git a/pandas/core/algorithms.py b/pandas/core/algorithms.py
index bbca78459ca75..5f7a6ed2a82a4 100644
--- a/pandas/core/algorithms.py
+++ b/pandas/core/algorithms.py
@@ -863,8 +863,10 @@ def value_counts_internal(
     dropna: bool = True,
 ) -> Series:
     from pandas import (
+        DatetimeIndex,
         Index,
         Series,
+        TimedeltaIndex,
     )
 
     index_name = getattr(values, "name", None)
@@ -929,6 +931,31 @@ 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 values.inferred_freq is not None
+            ):
+                # freq preservation
+                # Check if the result would be the same as input
+                if len(idx) == len(values) and idx.equals(values):
+                    # Rebuild idx with the correct type and inferred frequency
+                    if isinstance(values, DatetimeIndex):
+                        idx = DatetimeIndex(
+                            idx._data if hasattr(idx, "_data") else idx.values,
+                            freq=values.inferred_freq,
+                            name=idx.name,
+                        )
+
+                    elif isinstance(values, TimedeltaIndex):
+                        idx = TimedeltaIndex(
+                            idx._data if hasattr(idx, "_data") else idx.values,
+                            freq=values.inferred_freq,
+                            name=idx.name,
+                        )
+
             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..5e102c15f04f9 100644
--- a/pandas/tests/base/test_value_counts.py
+++ b/pandas/tests/base/test_value_counts.py
@@ -339,3 +339,153 @@ def test_value_counts_object_inference_deprecated():
     exp = dti.value_counts()
     exp.index = exp.index.astype(object)
     tm.assert_series_equal(res, exp)
+
+
+def _vc_make_index(kind: str, periods=5, freq="D"):
+    if kind == "dt":
+        return pd.date_range("2016-01-01", periods=periods, freq=freq)
+    if kind == "td":
+        return pd.timedelta_range(Timedelta(0), periods=periods, freq=freq)
+    raise ValueError("kind must be 'dt' or 'td'")
+
+
+@pytest.mark.parametrize(
+    "kind,freq,normalize",
+    [
+        ("dt", "D", False),
+        ("dt", "D", True),
+        ("td", "D", False),
+        ("td", "D", True),
+        ("td", Timedelta(hours=1), False),
+        ("td", Timedelta(hours=1), True),
+    ],
+)
+def test_value_counts_freq_preserved_datetimelike_no_sort(kind, freq, normalize):
+    idx = _vc_make_index(kind, periods=5, freq=freq)
+    vc = idx.value_counts(sort=False, normalize=normalize)
+    assert vc.index.freq == idx.freq
+    if normalize:
+        assert np.isclose(vc.values, 1 / len(idx)).all()
+
+
+@pytest.mark.parametrize(
+    "kind,freq",
+    [
+        ("dt", "D"),
+        ("td", "D"),
+        ("td", Timedelta(hours=1)),
+    ],
+)
+def test_value_counts_freq_drops_datetimelike_when_sorted(kind, freq):
+    idx = _vc_make_index(kind, periods=5, freq=freq)
+    vc = idx.value_counts()  # default sort=True (reorders)
+    assert vc.index.freq is None
+
+
+@pytest.mark.parametrize(
+    "kind,freq",
+    [
+        ("dt", "D"),
+        ("td", "D"),
+        ("td", Timedelta(hours=1)),
+    ],
+)
+def test_value_counts_freq_drops_datetimelike_with_duplicates(kind, freq):
+    base = _vc_make_index(kind, periods=5, freq=freq)
+    obj = base.insert(1, base[1])  # duplicate one label
+    vc = obj.value_counts(sort=False)
+    assert vc.index.freq is None
+
+
+@pytest.mark.parametrize(
+    "kind,freq",
+    [
+        ("dt", "D"),
+        ("td", "D"),
+        ("td", Timedelta(hours=1)),
+    ],
+)
+def test_value_counts_freq_drops_datetimelike_with_gap(kind, freq):
+    base = _vc_make_index(kind, periods=5, freq=freq)
+    obj = base.delete(2)  # remove one step to break contiguity
+    vc = obj.value_counts(sort=False)
+    assert vc.index.freq is None
+
+
+@pytest.mark.parametrize(
+    "kind,freq,dropna,expect_hasnans",
+    [
+        ("dt", "D", False, True),  # keep NaT
+        ("dt", "D", True, False),  # drop NaT
+        ("td", "D", False, True),
+        ("td", "D", True, False),
+        ("td", Timedelta(hours=1), False, True),
+        ("td", Timedelta(hours=1), True, False),
+    ],
+)
+def test_value_counts_freq_drops_datetimelike_with_nat(
+    kind, freq, dropna, expect_hasnans
+):
+    base = _vc_make_index(kind, periods=3, freq=freq)
+    obj = base.insert(1, pd.NaT)
+    vc = obj.value_counts(dropna=dropna, sort=False)
+    assert vc.index.freq is None
+    assert vc.index.hasnans is expect_hasnans
+
+
+@pytest.mark.parametrize(
+    "freq,start,periods,sort",
+    [
+        ("D", "2016-01-01", 5, False),
+        ("D", "2016-01-01", 5, True),
+        ("M", "2016-01", 6, False),  # MonthEnd
+        ("M", "2016-01", 6, True),
+        ("Q-DEC", "2016Q1", 4, False),  # QuarterEnd (Dec anchored)
+        ("Q-DEC", "2016Q1", 4, True),
+        ("Y-DEC", "2014", 3, False),  # YearEnd (Dec anchored)
+        ("Y-DEC", "2014", 3, True),
+    ],
+)
+def test_value_counts_period_freq_preserved_sort_and_nosort(freq, start, periods, sort):
+    pi = pd.period_range(start=start, periods=periods, freq=freq)
+    vc = pi.value_counts(sort=sort)
+    assert isinstance(vc.index, pd.PeriodIndex)
+    assert vc.index.dtype == pi.dtype
+    assert vc.index.freq == pi.freq
+
+
+def test_value_counts_period_freq_preserved_with_duplicates():
+    pi = pd.period_range("2016-01", periods=5, freq="M")
+    obj = pi.insert(1, pi[1])  # duplicate one label
+    vc = obj.value_counts(sort=False)
+    assert isinstance(vc.index, pd.PeriodIndex)
+    assert vc.index.dtype == pi.dtype
+    assert vc.index.freq == pi.freq
+
+
+def test_value_counts_period_freq_preserved_with_gap():
+    pi = pd.period_range("2016-01", periods=5, freq="M")
+    obj = pi.delete(2)  # remove one element
+    vc = obj.value_counts(sort=False)
+    assert isinstance(vc.index, pd.PeriodIndex)
+    assert vc.index.dtype == pi.dtype
+    assert vc.index.freq == pi.freq
+
+
+def test_value_counts_period_freq_preserved_with_normalize():
+    pi = pd.period_range("2016-01", periods=4, freq="M")
+    vc = pi.value_counts(normalize=True, sort=False)
+    assert isinstance(vc.index, pd.PeriodIndex)
+    assert vc.index.dtype == pi.dtype
+    assert vc.index.freq == pi.freq
+    assert np.isclose(vc.values, 1 / len(pi)).all()
+
+
+def test_value_counts_period_freq_preserved_with_nat_dropna_true():
+    pi = pd.period_range("2016-01", periods=5, freq="M")
+    obj = pi.insert(1, pd.NaT)
+    vc = obj.value_counts(dropna=True, sort=False)
+    assert not vc.index.hasnans
+    assert isinstance(vc.index, pd.PeriodIndex)
+    assert vc.index.dtype == pi.dtype
+    assert vc.index.freq == pi.freq