Jacinda Ardern said that genome sequencing has detected the Delta strain, and that it originated in NSW.
"We are dealing with the Delta variant ... our case has originated in Australia."
"Now the job is to work out how and when it got here,” Ms Ardern said.
The NZ Government will examine whether the positive case leaked from one of the country's managed isolation facilities
New Zealand has detected an additional two COVID cases, bringing the total in the current outbreak to seven.
Masks will also be made compulsory as part of the country's level 4 lockdown.
"It will be mandatory for everyone aged 12 and over to wear a mask when they are visiting any of the essential services that are currently open, including supermarkets, pharmacies and service stations."
The Director-General of Health, Dr Ashley Bloomfield has warned that modelling shows the outbreak could get worse.
"We could expect somewhere between 50 and 120 cases, according to modelling."
"It is very important that people restrict their movement," he said.