A top health professional says it's "disappointing" some border workers appear to be rejecting vaccination.
Professor Michael Baker told Newshub Sunday's case - known as case C - is low risk, as they were already in isolation following contact with case B who tested positive last week.
Both cases are workers at the Grand Millennium managed isolation facility.
It's the third case originating from the facility in recent weeks . Case A was a cleaner who tested positive on March 21 and case B is a security guard.
"The big question here is why this case [case C] and the previous case got infected at all," Professor Baker told Newshub.
"Of course it's been pointed out case B hadn't been vaccinated - so there will be questions around how this case came to be infected, and were they vaccinated?"
The Ministry of Health says Case B missed two scheduled vaccination appointments due to "personal reasons" - but gave no further explanation.
Baker says New Zealand is in a better place to eliminate COVID-19 than other countries.
"In countries pursuing elimination, the approach to vaccines is very different - people are dying every day in other parts of the world so the priority is the elderlty and the sick - in New Zealand the priority has always been the border."
But that makes it twice as disappointing if workers are refusing to be immunised, he says.
"This is really important for protecting the country and that's why there's been such a priority attached to this workforce so it is disappointing if we're hearing about frontline workers who are not vaccinated."
Prime Minister Jacinda Ardern has said all border workers must be vaccinated by the end of April or risk being moved on to other jobs.
"If in that period they're not vaccinated, they are redeployed, so that is really last call," she said.
"Let's just acknowledge that these are individuals who've been the first in the queue and the ramifications for them not being vaccinated are huge."
Officials from the Ministry of Health say 90 percent of border workers have been vaccinated - however it was unable to confirm how many employees there are at the border due to the "continuous" recruitment process.
Regardless of how many staff are vaccinated, Professor Baker says the priority is to trace the infection - and once the source is found, identify how to stop it reoccurring.
"Figure out what went wrong and stop it happening again."