It has been detected that malicious software is attempting to steal the details from customer credit cards in Centra, SuperValu and Daybreak.
The malicious software was recording debit and credit card numbers and expiry dates, but not the cardholder name, PIN number or CCV number.
Musgrave, owners of the three popular stores, have advised customers to check their bank statements for any unusual transactions.
Musgrave also said they have installed advanced technical fixes to combat the attempted breach.
The Gardaà and the Data Protection Commissioner are currently investigating.