Kiwibank has confirmed 4200 customers were sent the incorrect transaction history via email or internet banking.
The customers received a bank statement with their correct account number, name and address, but another person's transaction history.
The bank said it is investigating how the information went to the wrong customers and has asked those who received it to delete it immediately.
"We are also writing to customers whose transaction history may have been shared with the wrong person, apologising for the error and outlining the steps we've taken to protect their transaction history. We believe the impact on these customers is low, but we will work with them to address any concerns they have," the bank said in a statement.
It has also contacted the Privacy Commission to explain the error and how to fix the issue.
Kiwibank customer Dave Lesperance was one of those affected by the breach, he told RNZ he was concerned about who had received his private details.
"[Kiwibank] seemed to know that something had gone wrong but they couldn't tell me who had my details.
"I tried four times and four different people weren't too sure what was going on."
Lesperance said he was offered no advice by Kiwibank and was hung up on during one of his calls with the bank.
He said it was a horrible feeling thinking someone else had his information and that he will change banks because of it.