diff --git a/py-polars/polars/expr/expr.py b/py-polars/polars/expr/expr.py
index 68c013feaca8..258cbc802bf3 100644
--- a/py-polars/polars/expr/expr.py
+++ b/py-polars/polars/expr/expr.py
@@ -3845,8 +3845,16 @@ def wrap_f(x: Series) -> Series:  # pragma: no cover
         elif strategy == "threading":
 
             def wrap_threading(x: Series) -> Series:
+                def get_lazy_promise(df: DataFrame) -> LazyFrame:
+                    return df.lazy().select(
+                        F.col("x").map(wrap_f, agg_list=True, return_dtype=return_dtype)
+                    )
+
                 df = x.to_frame("x")
 
+                if x.len() == 0:
+                    return get_lazy_promise(df).collect().to_series()
+
                 n_threads = threadpool_size()
                 chunk_size = x.len() // n_threads
                 remainder = x.len() % n_threads
@@ -3858,11 +3866,6 @@ def wrap_threading(x: Series) -> Series:
                         for i in range(n_threads)
                     ]
 
-                def get_lazy_promise(df: DataFrame) -> LazyFrame:
-                    return df.lazy().select(
-                        F.col("x").map(wrap_f, agg_list=True, return_dtype=return_dtype)
-                    )
-
                 # create partitions with LazyFrames
                 # these are promises on a computation
                 partitions = []
diff --git a/py-polars/tests/unit/operations/test_apply.py b/py-polars/tests/unit/operations/test_apply.py
index d7948408cd2f..af6cb5946633 100644
--- a/py-polars/tests/unit/operations/test_apply.py
+++ b/py-polars/tests/unit/operations/test_apply.py
@@ -391,3 +391,25 @@ def test_apply_dict_order_10128() -> None:
 def test_apply_10237() -> None:
     df = pl.DataFrame({"a": [1, 2, 3]})
     assert df.select(pl.all().apply(lambda x: x > 50))["a"].to_list() == [False] * 3
+
+
+def test_apply_on_empty_col_10639() -> None:
+    df = pl.DataFrame({"A": [], "B": []})
+    res = df.groupby("B").agg(
+        pl.col("A")
+        .apply(lambda x: x, return_dtype=pl.Int32, strategy="threading")
+        .alias("Foo")
+    )
+    assert res.to_dict(False) == {
+        "B": [],
+        "Foo": [],
+    }
+    res = df.groupby("B").agg(
+        pl.col("A")
+        .apply(lambda x: x, return_dtype=pl.Int32, strategy="thread_local")
+        .alias("Foo")
+    )
+    assert res.to_dict(False) == {
+        "B": [],
+        "Foo": [],
+    }