Danske Bank underpaid or overcharged interest to more than 8,600 customers, it has emerged.
The bank has written the customers to inform them the money is being repaid.
Danske, which closed current accounts for customers earlier this year, said that the technical error arose between 16 December last year and 16 January this year.
As a result the interest was calculated incorrectly.
The development has affected 8,626 accounts and the average reimbursement was €1.83.
The bank has told customers it has identified the source of the error.
Danske said in a statement: "Only accounts where interest calculations apply (i.e. an overdraft or a credit interest bearing account) were affected. The error did not impact customers in terms of account balances."
It has repaid customers who had accounts open with Danske. For other clients who had already moved bank, Danske has offered to repay the interest to customers' new bank accounts.
It said if it does not hear from customers by 31 July it will donate the money to Our Lady's Childrens' Hospital in Crumlin.
In a statement the Central Bank said it was aware of the issue and its code requires errors to be resolved speedily and customers to be notified and refunded.