The bank said it was investigating a systems issue that is affecting online banking and some transactions.
"Our team is working hard to implement a fix to the system issues we're experiencing today," the bank wrote on its Facebook page, and said it did not yet have an estimated time for services to return to normal.
Customers were also complaining on the bank's Facebook page.
"Was just left standing completely embarrassed at a check out, lunch already eaten, card not working and unable to access app or internet banking," one person wrote.
"Not good enough," another wrote. "Away on holiday with family with no access to funds."
BNZ said it was working hard to resolve the problem and apologised for the inconvenience.
The bank said customers having trouble with PayWave could try inserting their card into pay terminals to see if that worked, although it cautioned it might not work for all transactions.
Customers were still able to get cash out of BNZ ATMs, the bank said.
