Musgraves are advising customers to check their bank statements after a cyber attack.
The company that owns SuperValu, Centra and Daybreak stores says the malicious software tried to extract debit and credit card details from its customers, but claims there is no evidence any data has been stolen.
Gardai and the Office of the Data Protection Commissioner are investigating.
It's not clear when the attack happened, but it's believed to have been in the last number of days.