Some customers of the BNZ have received incorrect messages from the bank telling them their accounts are thousands of dollars in the red.
The bank has received a number of online complaints from people who say they have received either an email or a text this morning telling them their accounts are overdrawn.
Rebecca Burk sent a query to the bank on Facebook after she received an alert for a home loan account with the bank - which she does not have.
"Is there a glitch in your notifications system this morning?. Received an email and TXT alert stating my rapid repay loan was overdrawn by several thousand dollars but I don't have a home loan with you! Whats up?"
Another customer queried the safety of her funds after receiving an email that appeared to be a hoax.
"I am a long time BNZ customer and this morning I have received an email supposedly from you telling me my bank account is seriously overdrawn.
"I immediately treated this as a hoax but you need to know as clearly you have been hacked! That being the case can you guarantee your customers funds are safe????" said a Facebook post by Jan McKenzie-Laurence.
A spokeswoman for the BNZ said a small number of customers had received routine text an email alerts for accounts that did not belong to them because of a system error.
"These alerts did not include customer account numbers or names."
She said the bank was still investigating the cause of the issue and apologised for the inconvenience.