Surfaces in a coolstore workplace are being tested to see whether international freight may have been the origin of the new cases.
One of the people who has tested positive for Covid-19 is an employee at an Americold coolstore in Mt Wellington, one of four people who tested positive on Tuesday.
The man had been off work on sick leave for nine days.
Americold NZ Managing Director Richard Winnall told the Herald the company was notified an employee was suspected of having Covid-19 late yesterday and that the Mt Wellington branch needed to close for 48 hours.
"We have made contact with him. He is doing okay. He has been on sick leave for the last nine days."
So far the source of New Zealand's first community transmission is unknown, with Director General of Health Ashley Bloomfield saying that authorities are "working hard to put together pieces of the puzzle on how this family got infected".
"We are very confident we didn't have any community transmission for a very long period," Bloomfield said this morning, adding: "We know the virus can survive within refrigerated environments for quite some time."
Four members of one family have so far tested positive for Covid-19.
Close contacts of the family are required to stay in isolation for 14 days regardless of a negative test.
Recently, there have been cases reported overseas of traces of the virus being found on frozen imports.
Reuters have reported that the city government of Yantai, a port city in China's eastern Shandong province, said it had found the virus on the packaging of frozen seafood that had arrived from the port city of Dalian, which recently battled a surge of cases.
Two of the new Covid cases travelled to Rotorua while showing virus symptoms and visited tourism spots.
The Ministry of Health is working to establish where they visited in Rotorua.
People in Rotorua would need to be vigilant, director general of health Ashley Bloomfield said.
If there is another case in Rotorua, a nationwide response will be necessary.
The woman, in her 20s, travelled out of Auckland last weekend. The woman and two young children visited tourist attractions, Bloomfield said.
None of the people who tested positive in the community needed hospital-level care, Bloomfield said.
"I know that the virus re-emerging in our community has caused alarm and the unknown is scary. That causes anxiety for many of us," Bloomfield said.
The family who had tested positive was in isolation at home in south Auckland and a decision hadn't been made about whether they would be moved to a quarantine facility, he said.
Meanwhile, a west Auckland medical centre has closed for 48 hours after one of the country's four new Covid-cases visited the clinic.
An email from Glen Eden's Westview Medical Centre to a patient, see by the Herald, says the patient was seen in the Infection Control area at the medical clinic and was wearing a mask.
One of the four new Covid cases with no links to overseas travel had a test at a West Auckland clinic.
"The patient was assessed and swabbed by one of our doctors wearing full protective equipment," the email said.
"All surfaces were subsequently cleaned as per guidelines. On the advice of the Ministry of Health, Westview will close down for 48hrs from 11am today 12/08/2020.
"Our doctors and nurses will contact all booked patients to offer phone consultations over the next 48hrs."
In the letter it said they apologised for the inconvenience but it was necessary to avoid New Zealand having to go back to level 4, "something none of us want to happen".
The Herald has contacted Westview Medical Centre and the Ministry of Health for comment and is awaiting a response.