Mr Thompson said the documents had been intended for the Kiwibank head office in Wellington and were given to a client in error.
"It was human error, it was a mistake."
The documents consisted of requests for changes to accounts. Mr Thompson said that when the documents were returned, the changes were made.
The bank had conducted a review and he reassured customers that they had "tightened up on procedures".
This breach of privacy was "very rare" and Mr Thompson said staff were "horrified" it had occurred.
As they were operating out of a temporary premises, some procedures had been changed, which contributed to the breach. The Post Shop is expected to move back to its original site on Tainui St next month.