diff --git a/doc/source/whatsnew/v3.0.0.rst b/doc/source/whatsnew/v3.0.0.rst
index 10d5a518f686d..b68f941dfbcc0 100644
--- a/doc/source/whatsnew/v3.0.0.rst
+++ b/doc/source/whatsnew/v3.0.0.rst
@@ -296,6 +296,7 @@ Bug fixes
 - Fixed bug in :meth:`DataFrame.to_string` that raised ``StopIteration`` with nested DataFrames. (:issue:`16098`)
 - Fixed bug in :meth:`DataFrame.update` bool dtype being converted to object (:issue:`55509`)
 - Fixed bug in :meth:`DataFrameGroupBy.apply` that was returning a completely empty DataFrame when all return values of ``func`` were ``None`` instead of returning an empty DataFrame with the original columns and dtypes. (:issue:`57775`)
+- Fixed bug in :meth:`GroupBy.median` where nat values gave an incorrect result. (:issue:`57926`)
 - Fixed bug in :meth:`Series.diff` allowing non-integer values for the ``periods`` argument. (:issue:`56607`)
 - Fixed bug in :meth:`Series.rank` that doesn't preserve missing values for nullable integers when ``na_option='keep'``. (:issue:`56976`)
 - Fixed bug in :meth:`Series.replace` and :meth:`DataFrame.replace` inconsistently replacing matching instances when ``regex=True`` and missing values are present. (:issue:`56599`)
diff --git a/pandas/_libs/groupby.pyi b/pandas/_libs/groupby.pyi
index 95ac555303221..53f5f73624232 100644
--- a/pandas/_libs/groupby.pyi
+++ b/pandas/_libs/groupby.pyi
@@ -12,6 +12,7 @@ def group_median_float64(
     min_count: int = ...,  # Py_ssize_t
     mask: np.ndarray | None = ...,
     result_mask: np.ndarray | None = ...,
+    is_datetimelike: bool = ...,  # bint
 ) -> None: ...
 def group_cumprod(
     out: np.ndarray,  # float64_t[:, ::1]
diff --git a/pandas/_libs/groupby.pyx b/pandas/_libs/groupby.pyx
index 2ff45038d6a3e..f3df54222a126 100644
--- a/pandas/_libs/groupby.pyx
+++ b/pandas/_libs/groupby.pyx
@@ -101,7 +101,11 @@ cdef float64_t median_linear_mask(float64_t* a, int n, uint8_t* mask) noexcept n
     return result
 
 
-cdef float64_t median_linear(float64_t* a, int n) noexcept nogil:
+cdef float64_t median_linear(
+    float64_t* a,
+    int n,
+    bint is_datetimelike=False
+) noexcept nogil:
     cdef:
         int i, j, na_count = 0
         float64_t* tmp
@@ -111,9 +115,14 @@ cdef float64_t median_linear(float64_t* a, int n) noexcept nogil:
         return NaN
 
     # count NAs
-    for i in range(n):
-        if a[i] != a[i]:
-            na_count += 1
+    if is_datetimelike:
+        for i in range(n):
+            if a[i] == NPY_NAT:
+                na_count += 1
+    else:
+        for i in range(n):
+            if a[i] != a[i]:
+                na_count += 1
 
     if na_count:
         if na_count == n:
@@ -125,6 +134,8 @@ cdef float64_t median_linear(float64_t* a, int n) noexcept nogil:
 
         j = 0
         for i in range(n):
+            if is_datetimelike and a[i] == NPY_NAT:
+                continue
             if a[i] == a[i]:
                 tmp[j] = a[i]
                 j += 1
@@ -170,6 +181,7 @@ def group_median_float64(
     Py_ssize_t min_count=-1,
     const uint8_t[:, :] mask=None,
     uint8_t[:, ::1] result_mask=None,
+    bint is_datetimelike=False,
 ) -> None:
     """
     Only aggregates on axis=0
@@ -228,7 +240,7 @@ def group_median_float64(
                 ptr += _counts[0]
                 for j in range(ngroups):
                     size = _counts[j + 1]
-                    out[j, i] = median_linear(ptr, size)
+                    out[j, i] = median_linear(ptr, size, is_datetimelike)
                     ptr += size
 
 
diff --git a/pandas/core/groupby/ops.py b/pandas/core/groupby/ops.py
index acf4c7bebf52d..8585ae3828247 100644
--- a/pandas/core/groupby/ops.py
+++ b/pandas/core/groupby/ops.py
@@ -415,6 +415,7 @@ def _call_cython_op(
                 "last",
                 "first",
                 "sum",
+                "median",
             ]:
                 func(
                     out=result,
@@ -427,7 +428,7 @@ def _call_cython_op(
                     is_datetimelike=is_datetimelike,
                     **kwargs,
                 )
-            elif self.how in ["sem", "std", "var", "ohlc", "prod", "median"]:
+            elif self.how in ["sem", "std", "var", "ohlc", "prod"]:
                 if self.how in ["std", "sem"]:
                     kwargs["is_datetimelike"] = is_datetimelike
                 func(
diff --git a/pandas/tests/groupby/test_groupby.py b/pandas/tests/groupby/test_groupby.py
index 00e781e6a7f07..2a9114d13c8ae 100644
--- a/pandas/tests/groupby/test_groupby.py
+++ b/pandas/tests/groupby/test_groupby.py
@@ -145,6 +145,13 @@ def test_len_nan_group():
     assert len(df.groupby(["a", "b"])) == 0
 
 
+def test_groupby_timedelta_median():
+    # issue 57926
+    df = DataFrame({"label": ["foo", "foo"], "timedelta": [pd.NaT, Timedelta("1d")]})
+    median = df.groupby("label")["timedelta"].median()
+    assert median.loc["foo"] == Timedelta("1d")
+
+
 @pytest.mark.parametrize("keys", [["a"], ["a", "b"]])
 def test_len_categorical(dropna, observed, keys):
     # GH#57595