Hunter's family believes she contracted the deadly virus during an outbreak that infected staff and patients.
Director general of health Ashley Bloomfield says Hunter's death will now be treated as being related to Covid-19.
Hunter had been confirmed as having Covid-19 in April and recovered in hospital and had two negative test results since then, he said. Health officials believed she had recovered from the virus.
Bloomfield also announced that there are no new Covid-19 cases today. Twelve more people have recovered in the past 24 hours. There are now only eight active cases.
It is now six days since a new case was discovered, a record since the start of the pandemic.
The total tally of confirmed and probable cases stands at 1504.
Second wave?
The World Health Organisation has reminded countries about relaxing restrictions as epidemics come in waves and another wave was a possibility in NZ for months to come.
A potential risk was aircrew coming into the country, said Bloomfield, and the Ministry of Health was working with airlines on ways to strengthen the current guidelines further, especially for flights that went further than Australia.
Bloomfield said the virus has a long tail and the death today shows how long the impact of the disease and how long after infection people had tested positive was why New Zealand would be at alert level 2 for a time.
New Zealand stepped into alert level 3 and 2 rapidly and relaxed mass gatherings, Bloomfield said.
Bloomfield said "it was safe to go back" to work now.
The recommendation for face masks on air travel was still that they're not required but not discouraged, he said.
It was hard for New Zealand to say we're on a pathway to eradication while the pandemic was ongoing overseas and New Zealand was looking at opening up the borders. The goal was still elimination, he said.
Forced vaccinations weren't in the ministry's thinking and Bloomfield said he didn't think that it would be required as he'd be surprised if "New Zealanders didn't get right in behind" the vaccination effort, if one was available.
Transtasman bubble
On the transtasman bubble, Bloomfield said from a health perspective it was the number of cases and the pattern of cases that they would be looking at in Australia and whether any risks could be managed in transit of people.
Once there's a degree of comfort in travel between states that it might be that they are comfortable in opening up the border to New Zealand.
The Pacific is also an option for opening the border, he said.
Bloomfield said "it was quite a complex operation" in the managed isolation hotels so if there was another accommodation facility was able to offer that level, that could be an option for students.