diff --git a/narwhals/_arrow/group_by.py b/narwhals/_arrow/group_by.py
index 5f0e4a4ca..1b102a297 100644
--- a/narwhals/_arrow/group_by.py
+++ b/narwhals/_arrow/group_by.py
@@ -120,16 +120,24 @@ def agg_arrow(
             function_name = remove_prefix(expr._function_name, "col->")
             function_name = POLARS_TO_ARROW_AGGREGATIONS.get(function_name, function_name)
             for root_name, output_name in zip(expr._root_names, expr._output_names):
-                if function_name != "len":
+                if function_name not in ("len", "count_distinct"):
                     simple_aggregations[output_name] = (
                         (root_name, function_name),
                         f"{root_name}_{function_name}",
                     )
-                else:
+                elif function_name == "len":
                     simple_aggregations[output_name] = (
                         (root_name, "count", pc.CountOptions(mode="all")),
                         f"{root_name}_count",
                     )
+                elif function_name == "count_distinct":
+                    simple_aggregations[output_name] = (
+                        (root_name, "count_distinct", pc.CountOptions(mode="all")),
+                        f"{root_name}_count_distinct",
+                    )
+                else:  # pragma: no cover
+                    msg = "unreachable code"
+                    raise RuntimeError(msg)
 
         aggs: list[Any] = []
         name_mapping = {}
diff --git a/tests/test_group_by.py b/tests/test_group_by.py
index 0134322c2..5c69983f4 100644
--- a/tests/test_group_by.py
+++ b/tests/test_group_by.py
@@ -121,7 +121,7 @@ def test_group_by_n_unique_w_missing(constructor: Any) -> None:
         .agg(
             nw.col("b").n_unique(),
             c_n_unique=nw.col("c").n_unique(),
-            c_n_unique_other=nw.col("c").n_unique(),
+            c_n_min=nw.col("b").min(),
             d_n_unique=nw.col("d").n_unique(),
         )
         .sort("a")
@@ -130,7 +130,7 @@ def test_group_by_n_unique_w_missing(constructor: Any) -> None:
         "a": [1, 2],
         "b": [2, 1],
         "c_n_unique": [1, 1],
-        "c_n_unique_other": [1, 1],
+        "c_n_min": [4, 5],
         "d_n_unique": [1, 1],
     }
     compare_dicts(result, expected)