AIB has had to refund customers and pay compensatory interest of €3.7m after it overcharged 6,855 clients, RTÉ News has learned.
The bank had failed to inform the customers in writing that their overdrafts had expired.
As a result the clients had been surcharged interest by the bank in error.
AIB has reported the issue to the Central Bank, with the average refund being around €543.
In a statement, AIB said it apologised for the error and the inconvenience caused.
It said it had made appropriate changes to procedures as a result of the issue and that the bank was writing to the affected customers, most of whom were business clients.
In a statement the Central Bank confirmed it was aware of the issue.
It said the Consumer Protection Code required errors to be resolved speedily and for customers to be notified and refunded appropriately.
The Central Bank did not say if it would take any further action.