Allied Irish Bank (AIB) says a computer error caused 15,000 payment advice slips - some featuring personal details including names, addresses and bank account and sort code numbers - to be sent to the wrong addresses.
In a statement the bank says that a "technical problem" led to 15,000 payment slips for deposits or withdrawals in foreign funds being issued to the wrong customers between 13 and 15 November.
About 11,000 individual customers are thought to be affected by the glitch.
Around half of payment slips are thought to have contained names, addresses and account and bank sort code numbers of other clients. The rest contained partial information such as account numbers and sort codes.
AIB says that no customer accounts have been incorrectly debited and all payments were processed in accordance with customer instructions.
The bank says it is writing to all affected customers and has informed the Data Protection Commissioner on the incident.
The news comes just days after it emerged that the UK's HM Revenue and Customs has lost confidential information - including bank account details - of all the country's 25 million child benefit recipients.
Earlier this year UK bank Hbos launched an investigation into how a customer who requested a copy of her bank statement ended up being sent the confidential details of 75,000 other account holders.
Stephanie McLaughlin had asked Hbos for one copy of her bank statement but received five packages containing 2500 sheets featuring other customers' names, sort codes and account details instead.