ANZ workers would either have to be vaccinated or undergo a rapid antigen test to work in branches under a proposal from the bank, its chief executive says.
But Antonia Watson says customers won't need to be vaccinated to come in.
"We haven't been designated as an essential business under the supermarket or pharmacy rules. But we still feel like we are.
"We can't exclude a vulnerable customer that needs to come in and get cash and has chosen not to be vaccinated."
Watson said its staff would still be wearing PPE, visors and masks.
The New Zealand Bankers Association sought guidance from the Government on whether banks were an essential service but they have been classified as general retail.
An NZBA spokesman said under that guidance retail was not required to use My Vaccine Passes, but if a business opted to require these, then it was recommended the business sight and/or verify customers' My Vaccine Passes.
He said that effectively meant it was up to each bank to decide whether or not it required vaccine passes for customers entering branches.
Other banks appear to be going down the same route as the ANZ.
A Westpac spokesman said that given its critical role in supporting communities, customers would be able to continue using its branches regardless of their vaccination status.
"However, we have begun talking to our people about a plan to make double vaccination a condition of entry for employees and contractors to Westpac locations around New Zealand.
"Visitors attending meetings and events at Westpac corporate sites would also need to be double vaccinated. We believe these measures will help keep the Westpac team and our customers safe."
He said Westpac staff who were not double vaccinated would be able to continue to work from home and attend events and meetings virtually, although no final decisions had been made on this yet.
A Kiwibank spokeswoman said it was following Ministry of Health guidelines and would be asking customers to scan in, wear a mask and respect social distancing when visiting a branch.
"We'll be adhering to the different traffic light settings and managing overall branch capacity limits. At this stage customers don't have to be vaccinated or show their vaccination status to do their banking with us. We continue to work through the changing settings and will share any updates for customers on our website."
A spokeswoman for the ASB said banks provided a vital service to New Zealanders.
"As such we don't require customers using ASB branches to provide evidence of vaccination.
"We do ask that customers sign in, wear masks and maintain social distancing when in our branches. Our teams are masked and socially distanced. We're also regularly cleaning in branches, including disinfecting Eftpos terminals and machines, and other high-touch spaces."
She said the bank supported vaccinations for its people was "currently in consultation with our teams about these issues".
A BNZ spokesman said it was constantly reviewing its policies and settings to ensure the best possible protection for its customers and people.
"Right now we do not require a customer to be vaccinated, but we have a number of controls in place in branches to keep people safe. These are aligned to the Ministry of Health guidance, including physical distancing between customers and our people, hygiene measures, contact tracing, and mask use. If our staff are unwell, they are asked to stay home."
He said the bank strongly encouraged its people to get vaccinated and gave them time off to do so.