COVID-19 response minister Chris Hipkins said the variant "changes the game considerably" and makes existing protections "look less adequate".
It comes as the country announced a further 21 confirmed cases in the latest outbreak of the virus.
New Zealand had quashed earlier COVID outbreaks with rapid, strict lockdowns.
The country was praised for its efforts, which effectively stopped the spread of the virus. Prime Minister Jacinda Ardern has repeatedly referred to New Zealand as "our team of five million".