The company says customers could have been a victim if they used a card to make a purchase at Aldi stores in Roselle on St. Georges Avenue and in Union on Commerce Avenue, between December 2023 and January 2024.
The other three stores affected by the breach were in California.
Aldi says it has taken new steps to secure payment systems.
Customers who believe they may have been a victim should call their credit card company.
For more information, customers can call 1-800-325-7894, Monday through Friday from 9 a.m. to 5 p.m.