diff --git a/doc/source/whatsnew/v3.0.0.rst b/doc/source/whatsnew/v3.0.0.rst
index 9089b9cdd2185..57ab2d65e4f7a 100644
--- a/doc/source/whatsnew/v3.0.0.rst
+++ b/doc/source/whatsnew/v3.0.0.rst
@@ -631,6 +631,7 @@ Datetimelike
 - Bug in :func:`date_range` where using a negative frequency value would not include all points between the start and end values (:issue:`56147`)
 - Bug in :func:`tseries.api.guess_datetime_format` would fail to infer time format when "%Y" == "%H%M" (:issue:`57452`)
 - Bug in :func:`tseries.frequencies.to_offset` would fail to parse frequency strings starting with "LWOM" (:issue:`59218`)
+- Bug in :meth:`DataFrame.min` and :meth:`DataFrame.max` casting ``datetime64`` and ``timedelta64`` columns to ``float64`` and losing precision (:issue:`60850`)
 - Bug in :meth:`Dataframe.agg` with df with missing values resulting in IndexError (:issue:`58810`)
 - Bug in :meth:`DatetimeIndex.is_year_start` and :meth:`DatetimeIndex.is_quarter_start` does not raise on Custom business days frequencies bigger then "1C" (:issue:`58664`)
 - Bug in :meth:`DatetimeIndex.is_year_start` and :meth:`DatetimeIndex.is_quarter_start` returning ``False`` on double-digit frequencies (:issue:`58523`)
diff --git a/pandas/core/nanops.py b/pandas/core/nanops.py
index d6154e2352c63..d1dc0ff809497 100644
--- a/pandas/core/nanops.py
+++ b/pandas/core/nanops.py
@@ -1093,11 +1093,14 @@ def reduction(
         if values.size == 0:
             return _na_for_min_count(values, axis)
 
+        dtype = values.dtype
         values, mask = _get_values(
             values, skipna, fill_value_typ=fill_value_typ, mask=mask
         )
         result = getattr(values, meth)(axis)
-        result = _maybe_null_out(result, axis, mask, values.shape)
+        result = _maybe_null_out(
+            result, axis, mask, values.shape, datetimelike=dtype.kind in "mM"
+        )
         return result
 
     return reduction
@@ -1499,6 +1502,7 @@ def _maybe_null_out(
     mask: npt.NDArray[np.bool_] | None,
     shape: tuple[int, ...],
     min_count: int = 1,
+    datetimelike: bool = False,
 ) -> np.ndarray | float | NaTType:
     """
     Returns
@@ -1520,7 +1524,10 @@ def _maybe_null_out(
             null_mask = np.broadcast_to(below_count, new_shape)
 
         if np.any(null_mask):
-            if is_numeric_dtype(result):
+            if datetimelike:
+                # GH#60646 For datetimelike, no need to cast to float
+                result[null_mask] = iNaT
+            elif is_numeric_dtype(result):
                 if np.iscomplexobj(result):
                     result = result.astype("c16")
                 elif not is_float_dtype(result):
diff --git a/pandas/tests/frame/test_reductions.py b/pandas/tests/frame/test_reductions.py
index 04b1456cdbea6..64e686d25faa7 100644
--- a/pandas/tests/frame/test_reductions.py
+++ b/pandas/tests/frame/test_reductions.py
@@ -1544,6 +1544,44 @@ def test_min_max_dt64_with_NaT(self):
         exp = Series([pd.NaT], index=["foo"])
         tm.assert_series_equal(res, exp)
 
+    def test_min_max_dt64_with_NaT_precision(self):
+        # GH#60646 Make sure the reduction doesn't cast input timestamps to
+        # float and lose precision.
+        df = DataFrame(
+            {"foo": [pd.NaT, pd.NaT, Timestamp("2012-05-01 09:20:00.123456789")]},
+            dtype="datetime64[ns]",
+        )
+
+        res = df.min(axis=1)
+        exp = df.foo.rename(None)
+        tm.assert_series_equal(res, exp)
+
+        res = df.max(axis=1)
+        exp = df.foo.rename(None)
+        tm.assert_series_equal(res, exp)
+
+    def test_min_max_td64_with_NaT_precision(self):
+        # GH#60646 Make sure the reduction doesn't cast input timedeltas to
+        # float and lose precision.
+        df = DataFrame(
+            {
+                "foo": [
+                    pd.NaT,
+                    pd.NaT,
+                    to_timedelta("10000 days 06:05:01.123456789"),
+                ],
+            },
+            dtype="timedelta64[ns]",
+        )
+
+        res = df.min(axis=1)
+        exp = df.foo.rename(None)
+        tm.assert_series_equal(res, exp)
+
+        res = df.max(axis=1)
+        exp = df.foo.rename(None)
+        tm.assert_series_equal(res, exp)
+
     def test_min_max_dt64_with_NaT_skipna_false(self, request, tz_naive_fixture):
         # GH#36907
         tz = tz_naive_fixture