The new rule will apply from the middle of next month, applying to all passengers aged 12 and over.
"Delta has really upped the stakes. What once kept us safe is no longer enough and we need an extra layer of protection," Air NZ chief executive Greg Foran said in a statement. "That's why we're taking a step further to keep our customers safe while allowing all Kiwis to fly."
He said the airline was aiming to have the change in place by December 14, for an initial period until March 31.
"For the most seamless experience, we're encouraging customers to download our Air New Zealand mobile app to make it easy as possible to connect their vaccination status in the Government's My Vaccine Pass with booking details, which will allow check-in."
People not fully vaccinated would need to provide evidence of a negative COVID-19 test 72 hours before departure, the national carrier said.
It comes after the airline last month confirmed it planned to require customers travelling anywhere on its international network to be fully vaccinated.