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Officials are now investigating whether it is an historic case or a false positive test result.
As a precaution, the Rakiura Rugrats early childhood centre has been closed for the rest of the week.
At a press conference with Prime Minister Jacinda Ardern today, Director-general of health Dr Ashley Bloomfield said the case was a child and it was likely the result was a false positive.
The result came as a family had Covid tests before planning to head overseas.
"Everything points to this being a false positive," Bloomfield said, but officials wanted to confirm this with serology testing now under way.
Bloomfield said that during the lockdown period last year there were quite a few Covid cases that health teams never knew about.
That meant the Stewart Island positive test could be a historical case.
Stewart Island/Rakiura local board chair Jon Spraggon said he was informed this morning of the existence of the weak positive case.
Spraggon was told that health officials would be visiting the island this afternoon.
"While the investigation is under way, as a precaution, a local childcare centre is being closed for the rest of the week," the Ministry of Health said.
The centre manager declined to comment.
Southland District Mayor Gary Tong said he was contacted at 8am today to be told the news of the test result.
''So we had a briefing to say that there was a team going down to do some swabs because of the result of this young person.''
Everything was to continue operating as normal while the Ministry of Health went through their protocols, he said.
''We'll all keep communicating at a high level and keep our community as informed as we can,'' he said.
''We'll remain positive and wait on the results of the tests.''
The principal of Halfmoon Bay School/ Te Kura o Rakiura, Kath Johnson, declined to comment and directed questions to Southern District Health Board.
Stewart Island resident Maureen Jones, who said she was in her 80s, was not concerned about the test result.
"We're doing extremely well that we haven't had it here before, with the amount of visitors we've had,'' she said.
She had a mask and was taking care of herself, but was not planning on going to get a test.
Earlier today, the ministry said a person with an "indeterminate test result" for Covid on Stewart Island was under investigation to determine whether they were infected or not.
A subsequent repeat test was negative. Their family members had also tested negative.
Possible local contacts had been asked to isolate until further information was available and a community testing station would open from 1pm today at the island's Community Centre.
"Given the isolated nature of the community the DHB is putting additional staff on the ground in Stewart Island today to provide testing, primarily for those in the community with symptoms and for anyone linked to the childcare centre.
"Any local residents seeking testing are expected to be able to be accommodated."
Real Journeys general manager Paul Norris said as soon as staff heard there was a potential case on the island, its Covid-19 response team was put into action.
''I contacted the Southland District Council and Ministry of Health to offer our full assistance with any travel or logistics to the island to undertake the testing.''
The company, which operates the ferry to Stewart Island from Bluff, had a few cancellations and it was happy to rebook or refund anyone who had concerns about travelling to the island.
Staff were also being offered support.
It was the quietest business time of the year on the island with none of the company's other experiences operating at present, he said.
Pop-up testing clinic open
The Southern District Health Board (SDHB) in a post on social media said a Covid-19 pop-up testing clinic would be open at the island's community centre from 1pm.
People who had cold and flu like symptoms, or who were feeling unwell, were asked to attend this afternoon’s clinic for a test. No appointment was necessary.
People who attended or visited the childcare centre the child attended were also being asked to have a test – even if they did not have symptoms.
SDHB Medical Officer of Health Dr Michael Butchard said anyone with cold or flu-like symptoms should stay at home until they were feeling well.
Personal hygiene, including regular handwashing and cough/sneeze etiquette should also be maintained.
If people had questions about their symptoms, they could call the Covid-19 testing call centre on 0800 VIRUS19 (0800 847 8719).
Flights still operating
Stewart Island Flights director Bill Moffat said flights to the island were still operating as normal.
He had not been contacted by the Ministry of Health.
''We're just waiting to hear of anything further from Ministry of Health of where to go to from here.''
Mr Moffat said the announcement had created a great amount of uncertainty amongst travellers but believed the case was a false positive.
''It would be an unusual place for it to start from,'' he said.
Invercargill Airport general manager Nigel Finnerty said there were no changes to the way it was doing business today.
''We're just operating as normal.''
He had received no information from the ministry.
Two new cases in MIQ
Meanwhile, the ministry said there were no new cases of in the community in New Zealand today.
There are two new cases in managed isolation facilities.
The two people who were being treated for the virus at Middlemore Hospital have now been discharged and taken back to Auckland’s quarantine facility.
- additional reporting Karen Pasco/Daisy Hudson