diff --git a/py-polars/polars/_utils/getitem.py b/py-polars/polars/_utils/getitem.py
index 05404437c0ce..364da0ff91f8 100644
--- a/py-polars/polars/_utils/getitem.py
+++ b/py-polars/polars/_utils/getitem.py
@@ -291,6 +291,9 @@ def _select_rows(
 ) -> DataFrame | Series:
     """Select one or more rows from the DataFrame."""
     if isinstance(key, int):
+        if key >= len(df):
+            msg = f"index {key} is out of bounds for DataFrame of height {len(df)}"
+            raise IndexError(msg)
         return df.slice(key, 1)
 
     if isinstance(key, slice):
diff --git a/py-polars/tests/unit/dataframe/test_df.py b/py-polars/tests/unit/dataframe/test_df.py
index 8c2fafcdd279..6fd66aa5bb3d 100644
--- a/py-polars/tests/unit/dataframe/test_df.py
+++ b/py-polars/tests/unit/dataframe/test_df.py
@@ -2995,3 +2995,21 @@ def test_get_column_after_drop_20119() -> None:
     df.drop_in_place("a")
     c = df.get_column("c")
     assert_series_equal(c, pl.Series("c", ["C"]))
+
+
+def test_select_oob_row_20775() -> None:
+    df = pl.DataFrame({"a": [1, 2, 3]})
+    with pytest.raises(
+        IndexError,
+        match="index 99 is out of bounds for DataFrame of height 3",
+    ):
+        df[99]
+
+
+def test_select_oob_element_20775() -> None:
+    df = pl.DataFrame({"a": [1, 2, 3]})
+    with pytest.raises(
+        IndexError,
+        match="index 99 is out of bounds for sequence of length 3",
+    ):
+        df[99, "a"]