Kiwi comedian Melanie Bracewell, who is currently in LA and is a BNZ customer, said in a tweet that her card declined while trying to buy a SIM card.
A Herald reporter said she had tried to use her Eftpos card a couple of times while shopping and it declined despite her having money in her account.
She tried to check her account on the BNZ app but couldn't log in so then phoned BNZ and was told the systems had been down for about an hour and a half and the outage was affecting all of the bank's customers.
"It's definitely not ideal for a Saturday," a BNZ staff member told the reporter on the phone.
A frustrated BNZ customer told the Herald the bank's Northwest branch was closed and staff were turning away customers at the door.
Other customers have posted on social media that they had been affected.
Over the ditch, customers of BNZ's parent company, NAB, also took to social media to complain about the outage, which is affecting internet and mobile banking, ATMs and Eftpos, news.com.au reported.
Aussie customers and businesses expressed embarrassment and frustration over the issue when people were left unable to pay for purchases
A BNZ spokesman said the bank was sorry for the inconvenience to customers and thanked them for their patience.