diff --git a/datafusion/functions-nested/src/min_max.rs b/datafusion/functions-nested/src/min_max.rs
index 2e7a32ba314e..210b5c3d9b5d 100644
--- a/datafusion/functions-nested/src/min_max.rs
+++ b/datafusion/functions-nested/src/min_max.rs
@@ -19,7 +19,7 @@
 use crate::utils::make_scalar_function;
 use arrow::array::{
     Array, ArrayRef, ArrowNativeTypeOp, ArrowPrimitiveType, AsArray, GenericListArray,
-    OffsetSizeTrait, PrimitiveBuilder, downcast_primitive,
+    OffsetSizeTrait, PrimitiveBuilder, downcast_primitive, new_empty_array,
 };
 use arrow::buffer::NullBuffer;
 use arrow::datatypes::DataType;
@@ -209,6 +209,12 @@ fn array_min_max_helper<O: OffsetSizeTrait>(
         return result;
     }
 
+    // `ScalarValue::iter_to_array` below cannot build an array from an empty
+    // iterator, so return an empty array of the element type for zero rows.
+    if array.is_empty() {
+        return Ok(new_empty_array(&array.value_type()));
+    }
+
     // Fallback: per-row ScalarValue path for non-primitive types
     let agg_fn = if is_min { min_batch } else { max_batch };
     let null_value = ScalarValue::try_from(array.value_type())?;
@@ -311,3 +317,106 @@ fn scalar_min_max<N: ArrowNativeTypeOp>(
     }
     best
 }
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+    use arrow::array::{GenericListBuilder, ListArray, StringArray, StringBuilder};
+    use arrow::datatypes::Int64Type;
+
+    fn utf8_list<O: OffsetSizeTrait>(
+        rows: Vec<Option<Vec<Option<&str>>>>,
+    ) -> GenericListArray<O> {
+        let mut builder = GenericListBuilder::<O, _>::new(StringBuilder::new());
+        for row in rows {
+            match row {
+                Some(values) => {
+                    for v in values {
+                        builder.values().append_option(v);
+                    }
+                    builder.append(true);
+                }
+                None => builder.append(false),
+            }
+        }
+        builder.finish()
+    }
+
+    #[test]
+    fn zero_rows_non_primitive_returns_empty_array() -> Result<()> {
+        for is_min in [true, false] {
+            let out = array_min_max_helper(&utf8_list::<i32>(vec![]), is_min)?;
+            assert_eq!(out.len(), 0);
+            assert_eq!(out.data_type(), &DataType::Utf8);
+
+            let out = array_min_max_helper(&utf8_list::<i64>(vec![]), is_min)?;
+            assert_eq!(out.len(), 0);
+            assert_eq!(out.data_type(), &DataType::Utf8);
+        }
+        Ok(())
+    }
+
+    #[test]
+    fn zero_rows_primitive_returns_empty_array() -> Result<()> {
+        let empty = ListArray::from_iter_primitive::<Int64Type, _, _>(Vec::<
+            Option<Vec<Option<i64>>>,
+        >::new());
+        for is_min in [true, false] {
+            let out = array_min_max_helper(&empty, is_min)?;
+            assert_eq!(out.len(), 0);
+            assert_eq!(out.data_type(), &DataType::Int64);
+        }
+        Ok(())
+    }
+
+    #[test]
+    fn non_primitive_rows() -> Result<()> {
+        let list = utf8_list::<i32>(vec![
+            Some(vec![Some("prod"), Some("api")]),
+            Some(vec![]),
+            None,
+            Some(vec![Some("web"), None, Some("db")]),
+        ]);
+        let min = array_min_max_helper(&list, true)?;
+        let max = array_min_max_helper(&list, false)?;
+        assert_eq!(
+            min.as_string::<i32>(),
+            &StringArray::from(vec![Some("api"), None, None, Some("db")])
+        );
+        assert_eq!(
+            max.as_string::<i32>(),
+            &StringArray::from(vec![Some("prod"), None, None, Some("web")])
+        );
+        Ok(())
+    }
+
+    #[test]
+    fn invoke_on_zero_row_batch() -> Result<()> {
+        // What ProjectionExec / TopK do when an upstream operator emits a
+        // zero-row batch.
+        let list: ArrayRef = Arc::new(utf8_list::<i32>(vec![]));
+        for udf in [array_min_udf(), array_max_udf()] {
+            let out = udf.invoke_with_args(ScalarFunctionArgs {
+                args: vec![ColumnarValue::Array(Arc::clone(&list))],
+                arg_fields: vec![Arc::new(arrow::datatypes::Field::new(
+                    "a",
+                    list.data_type().clone(),
+                    true,
+                ))],
+                number_rows: 0,
+                return_field: Arc::new(arrow::datatypes::Field::new(
+                    "r",
+                    DataType::Utf8,
+                    true,
+                )),
+                config_options: Arc::new(Default::default()),
+            })?;
+            let ColumnarValue::Array(out) = out else {
+                panic!("expected an array")
+            };
+            assert_eq!(out.len(), 0);
+            assert_eq!(out.data_type(), &DataType::Utf8);
+        }
+        Ok(())
+    }
+}