diff --git a/tests/queries/0_stateless/01603_insert_select_too_many_parts.sql b/tests/queries/0_stateless/01603_insert_select_too_many_parts.sql
index a56b680e212..0c33c1d6b18 100644
--- a/tests/queries/0_stateless/01603_insert_select_too_many_parts.sql
+++ b/tests/queries/0_stateless/01603_insert_select_too_many_parts.sql
@@ -3,6 +3,8 @@ CREATE TABLE too_many_parts (x UInt64) ENGINE = MergeTree ORDER BY tuple() SETTI
 
 SYSTEM STOP MERGES too_many_parts;
 SET max_block_size = 1, min_insert_block_size_rows = 0, min_insert_block_size_bytes = 0;
+-- Avoid concurrent partse check to avoid flakiness
+SET max_threads=1, max_insert_threads=1;
 
 -- exception is not thrown if threshold is exceeded when multi-block INSERT is already started.
 INSERT INTO too_many_parts SELECT * FROM numbers(10);