A teacher at Auckland's Avondale College is among the new cases of COVID-19 identified overnight - four of whom are flatmates on the North Shore, Director-General of Health Ashley Bloomfield says.
Another case is the teacher's sister, the NZ Herald reported, who is a nurse at Auckland City Hospital.
In a message to parents, Avondale College said all staff and students were considered close contacts and must self-isolate for two weeks.
"Even if New Zealand's national alert level changes from the current level 4, you must still complete your full 14-day self-isolation," the school said.
At Wedneday's COVID-19 news briefing Dr Bloomfield said two more people had tested positive for COVID-19 - in addition to the four flatmates identified earlier in the morning and the original infection found on Tuesday.
He said one of the flatmates went to work at Avondale College on Monday and another worked at Auckland City Hospital that same day.
Two other important locations of interest were Church of Christ in Freemans Bay and the SkyCity Casino - where one of the cases visited on Saturday, Dr Bloomfield said.
All of the new infections are linked to the original case - a 58-year-old man who tested positive for the Delta variant in the Auckland suburb of Devonport. After that case was detected on Tuesday night, the Coromandel - where the man visited over the weekend - and Auckland were placed into a week-long alert level 4 lockdown.
The rest of New Zealand faces level 4 restrictions for at least three days, but this period may be extended.
Speaking to Newshub, University of Otago public health professor Michael Baker said more COVID-19 infections are inevitable.
"There could be scores of cases now - who are only going to come forward in the next few days and be identified," he said.
Extra COVID-19 testing stations are being put up across Auckland and Coromandel with wait times said to be exceeding four hours.