Emergency services were called to the four-storey Loafers Lodge hostel in Wellington just after midnight local time (12:30 GMT Monday).
More than 50 people were rescued from the building, but police said 11 people remained unaccounted for.
PM Chris Hipkins warned the number of dead was likely to increase.
Police added that they could not be more specific on the number of deaths until they could access the building.
Upon arrival at the scene, firefighters found the top level of the building ablaze. By 04:00 at least 20 fire trucks had been deployed to extinguish it.
Fire and Emergency District commander Nick Pyatt described the fire as Wellington's "worst nightmare".
Mr Pyatt also said the building contained asbestos and urged locals to wear a face mask and keep their windows closed to avoid inhaling the smoke, the New Zealand Herald reported.
"This is a tragic event for all involved. My heartfelt condolences go to the loved ones of those who have lost their lives", he said.
Authorities rescued at least five people from the roof of the burning building, while one person sustained serious injuries after jumping from the third floor of the building to escape the flames, local media reported.
"Two of my mates have made it out, but the way things are looking for probably four other people I know in there, I don't know," said former Loafers resident Mark Lilly, in comments made to AFP.
Loafers Lodge Hostel has 92 rooms in total and caters to both short and long-term guests.
It was designated by New Zealand's Ministry of Social Development in 2011 as an emergency accommodation provider. Official figures show that more than 3,300 households currently live in emergency housing as of February.
Loafers customers range from shift workers like nurses and hospital staff to unemployed and homeless people, according to local media reports.
Several residents are people who have been deported from Australia, with some still unaccounted for.
The cause of the blaze is currently unknown, but police are reportedly investigating whether it was deliberately lit.
In comments to local media, Mr Hipkins called the fire "an absolute tragedy" and paid tribute to local firefighters "who have put themselves in harm's way over past hours to get people out of the building and put the fire out".
BBC