Around 110,000 AIB customers are to receive letters informing them they may be entitled to compensation as a result of a review of their card protection insurance policies.
The bank says customers may have been provided with insufficient information when they purchased the product, meaning they were paying for an element of cover for unauthorised or fraudulent use, that the bank was already covering.
The card protection is an optional policy with a premium of €16 a year.
The scheme was provided by Pinnacle Insurance plc and may have been selected by customers when applying for an AIB credit card.
AIB says it has engaged with the Central Bank to establish a voluntary redress scheme for all customers who purchased the CP policy from 1 August 2006.
All customers will given the opportunity to claim a refund of premiums paid.
The Central Bank's Director of Consumer Protection, Bernard Sheridan, said: "We require all firms to make full disclosure to consumers of all relevant material information when selling any financial product.
"It is important that consumers can have confidence that firms are acting in their best interests and that they are not sold any cover which they do not need.
"Where this has occurred it is our priority to ensure that consumers receive full redress. We encourage all affected consumers to make a claim."
The Central Bank says that if consumers do not receive a letter from AIB by 30 September, but think they have been affected, they should contact the bank directly.
Further details of how to claim under AIB's voluntary redress scheme, including contact details, can be found on its website.