"We believe the impact on these customers is low, but we will work with them to address any concerns they have."
The bank had also contacted the Privacy Commissioner over the breach.
"We have contacted the Privacy Commission to explain what has happened and how we have moved quickly to address this issue."
A spokesman for the Privacy Commissioner said it was notified by Kiwibank of the privacy breach yesterday afternoon.
"Any affected individuals can complain to our office if they have been harmed by the breach."
Kiwibank is 53 per cent owned by NZ Post, 25 per cent by the New Zealand Superannuation Fund and 22 per cent by ACC.
In February it posted an 18 per cent fall in its half-year net profit to $51 million for the six months to December.