diff --git a/crates/polars-plan/src/plans/conversion/functions.rs b/crates/polars-plan/src/plans/conversion/functions.rs
index 409da958477d..f77cb0e79a95 100644
--- a/crates/polars-plan/src/plans/conversion/functions.rs
+++ b/crates/polars-plan/src/plans/conversion/functions.rs
@@ -16,11 +16,12 @@ pub(super) fn convert_functions(
 ) -> PolarsResult<Node> {
     match function {
         // This can be created by col(*).is_null() on empty dataframes.
-        FunctionExpr::Boolean(BooleanFunction::AllHorizontal | BooleanFunction::AnyHorizontal)
-            if input.is_empty() =>
-        {
+        FunctionExpr::Boolean(BooleanFunction::AllHorizontal) if input.is_empty() => {
             return to_aexpr_impl(lit(true), arena, state);
         },
+        FunctionExpr::Boolean(BooleanFunction::AnyHorizontal) if input.is_empty() => {
+            return to_aexpr_impl(lit(false), arena, state);
+        },
         // Convert to binary expression as the optimizer understands those.
         // Don't exceed 128 expressions as we might stackoverflow.
         FunctionExpr::Boolean(BooleanFunction::AllHorizontal) => {
diff --git a/py-polars/tests/unit/operations/aggregation/test_horizontal.py b/py-polars/tests/unit/operations/aggregation/test_horizontal.py
index bc2bf2abbf46..b4054c695979 100644
--- a/py-polars/tests/unit/operations/aggregation/test_horizontal.py
+++ b/py-polars/tests/unit/operations/aggregation/test_horizontal.py
@@ -7,6 +7,7 @@
 import pytest
 
 import polars as pl
+import polars.selectors as cs
 from polars.exceptions import ComputeError
 from polars.testing import assert_frame_equal, assert_series_equal
 
@@ -51,6 +52,20 @@ def test_all_any_horizontally() -> None:
     assert "horizontal" not in dfltr.explain().lower()
 
 
+def test_empty_all_any_horizontally() -> None:
+    # any/all_horizontal don't allow empty input, but we can still trigger this
+    # by selecting an empty set of columns with pl.selectors.
+    df = pl.DataFrame({"x": [1, 2, 3]})
+    assert_frame_equal(
+        df.select(pl.any_horizontal(cs.string().is_null())),
+        pl.DataFrame({"literal": False}),
+    )
+    assert_frame_equal(
+        df.select(pl.all_horizontal(cs.string().is_null())),
+        pl.DataFrame({"literal": True}),
+    )
+
+
 def test_all_any_single_input() -> None:
     df = pl.DataFrame({"a": [0, 1, None]})
     out = df.select(