diff --git a/doc/source/whatsnew/v1.2.0.rst b/doc/source/whatsnew/v1.2.0.rst
index b43ed2963577d..fb6a238218e9f 100644
--- a/doc/source/whatsnew/v1.2.0.rst
+++ b/doc/source/whatsnew/v1.2.0.rst
@@ -515,6 +515,7 @@ Groupby/resample/rolling
 - Bug in :meth:`DataFrameGroupBy.rolling` returned wrong values with timeaware window containing ``NaN``. Raises ``ValueError`` because windows are not monotonic now (:issue:`34617`)
 - Bug in :meth:`Rolling.__iter__` where a ``ValueError`` was not raised when ``min_periods`` was larger than ``window`` (:issue:`37156`)
 - Using :meth:`Rolling.var()` instead of :meth:`Rolling.std()` avoids numerical issues for :meth:`Rolling.corr()` when :meth:`Rolling.var()` is still within floating point precision while :meth:`Rolling.std()` is not (:issue:`31286`)
+- Bug in :meth:`df.groupby(..).quantile() <pandas.core.groupby.DataFrameGroupBy.quantile>` and :meth:`df.resample(..).quantile() <pandas.core.resample.Resampler.quantile>` raised ``TypeError`` when values were of type ``Timedelta`` (:issue:`29485`)
 - Bug in :meth:`Rolling.median` and :meth:`Rolling.quantile` returned wrong values for :class:`BaseIndexer` subclasses with non-monotonic starting or ending points for windows (:issue:`37153`)
 
 Reshaping
diff --git a/pandas/core/groupby/groupby.py b/pandas/core/groupby/groupby.py
index 5d9028adb7372..c5bc9b563ea5e 100644
--- a/pandas/core/groupby/groupby.py
+++ b/pandas/core/groupby/groupby.py
@@ -60,6 +60,7 @@ class providing the base-class of operations.
     is_numeric_dtype,
     is_object_dtype,
     is_scalar,
+    is_timedelta64_dtype,
 )
 from pandas.core.dtypes.missing import isna, notna
 
@@ -2173,6 +2174,9 @@ def pre_processor(vals: np.ndarray) -> Tuple[np.ndarray, Optional[Type]]:
             elif is_datetime64_dtype(vals.dtype):
                 inference = "datetime64[ns]"
                 vals = np.asarray(vals).astype(float)
+            elif is_timedelta64_dtype(vals.dtype):
+                inference = "timedelta64[ns]"
+                vals = np.asarray(vals).astype(float)
 
             return vals, inference
 
diff --git a/pandas/tests/groupby/test_quantile.py b/pandas/tests/groupby/test_quantile.py
index 14b0d9ab60e52..e48f10ebacb79 100644
--- a/pandas/tests/groupby/test_quantile.py
+++ b/pandas/tests/groupby/test_quantile.py
@@ -236,3 +236,21 @@ def test_groupby_quantile_skips_invalid_dtype(q):
     result = df.groupby("a").quantile(q)
     expected = df.groupby("a")[["b"]].quantile(q)
     tm.assert_frame_equal(result, expected)
+
+
+def test_groupby_timedelta_quantile():
+    # GH: 29485
+    df = DataFrame(
+        {"value": pd.to_timedelta(np.arange(4), unit="s"), "group": [1, 1, 2, 2]}
+    )
+    result = df.groupby("group").quantile(0.99)
+    expected = DataFrame(
+        {
+            "value": [
+                pd.Timedelta("0 days 00:00:00.990000"),
+                pd.Timedelta("0 days 00:00:02.990000"),
+            ]
+        },
+        index=pd.Index([1, 2], name="group"),
+    )
+    tm.assert_frame_equal(result, expected)
diff --git a/pandas/tests/resample/test_timedelta.py b/pandas/tests/resample/test_timedelta.py
index 4783d806f8023..1c440b889b146 100644
--- a/pandas/tests/resample/test_timedelta.py
+++ b/pandas/tests/resample/test_timedelta.py
@@ -165,3 +165,22 @@ def test_resample_with_timedelta_yields_no_empty_groups():
         index=pd.timedelta_range(start="1s", periods=13, freq="3s"),
     )
     tm.assert_frame_equal(result, expected)
+
+
+def test_resample_quantile_timedelta():
+    # GH: 29485
+    df = DataFrame(
+        {"value": pd.to_timedelta(np.arange(4), unit="s")},
+        index=pd.date_range("20200101", periods=4, tz="UTC"),
+    )
+    result = df.resample("2D").quantile(0.99)
+    expected = DataFrame(
+        {
+            "value": [
+                pd.Timedelta("0 days 00:00:00.990000"),
+                pd.Timedelta("0 days 00:00:02.990000"),
+            ]
+        },
+        index=pd.date_range("20200101", periods=2, tz="UTC", freq="2D"),
+    )
+    tm.assert_frame_equal(result, expected)