Director-General of Health Dr Ashley Bloomfield says the ministry continues to adapt its response.
Bloomfield told Morning Report there were no new cases of Covid-19 to report overnight.
"That doesn't mean they haven't been processing a lot of tests. There were many hundreds if not into the thousands taken yesterday - a great response from Wellingtonians."
Bloomfield said the ministry would be watching closely at results today and tomorrow.
He said the Sydney lab processing the genomic data is behind in its workload due to staff being off sick. Hence the variant of the virus is not yet confirmed.
However, going by the person's epidemiological link to the New South Wales cluster, Bloomfield said it was most likely the Delta variant.
He said the person worked at a health facility in Sydney, and someone linked to the cluster had visited it.
"There's a clear epidemiological link and our colleagues in New South Wales are very confident about that."
There have been changes to the locations of interest.
Those who were at 4 Kings Bar at Jack Hacketts, 5 Inglewood Place, on 19 June between 8.45pm and 12am are asked to isolate for 14 days, test on day five and 12 since last exposure, and call Healthline.
Those who were at Jack Hackett's bar are asked to get a test on day 5 since last exposure and stay at home until a negative test result. They must also watch out for Covid-19 symptoms for 14 days.
Bloomfield said the person was in one of the bars for a long time.
"Places where there's close contact, crowded in a confined space, that's the higher risk."
The men's toilets at the southern end of the domestic concourse at Wellington Airport have been added as a location of interest. Anyone who used the toilets between 9.15am and 9.30am on Monday should stay home until a negative test result is received, and then monitor symptoms for a further 14 days.
As for wastewater testing, he said samples were being taken every day.
The last test on 21 June came back negative. The next results are expected later today.
"That's quite an important bit of information in terms of building that picture. The wastewater testing now is very sensitive.
"It's routinely positive up in Auckland from the western interceptor which ... Jet Park, the quarantine facility flows into. We've had a one-off positive result in Christchurch when there have been positive cases in the quarantine facility there.
"So it is very sensitive and it will help us with the picture and if those results are coming back negative [in Wellington] that also helps reassure us that we haven't got any Covid out in the community."
Health experts say they are mystified over the government's reluctance to enforce mandatory mask wearing and QR code scanning under alert level 2.
He said the ministry would continue to adapt its response as the pandemic progresses.
It is working to provide more advice to Cabinet on the wider use of masks and mandatory scanning of QR codes.
"It'll be up to Cabinet to decide that. I know the minister will keep people informed about that."
Prime Minister Jacinda Ardern told Morning Report mandatory QR scanning had never been off the table but there were enforcement logistics to work through. She said expanding the guidelines for mandatory mask would be too prescriptive.