Sixteen of the 18 crew of the Spanish-flagged Playa Zahara have tested positive.
A Ministry of Health spokesperson said on arrival at Lyttelton Port, 13 of them will be moved to a quarantine facility in Christchurch.
This includes the two people who returned negative results.
Managed Isolation and Quarantine deputy chief executive Megan Main told RNZ's Morning Report her team was waiting to hear from health authorities about where the crew would stay.
"We don't make the decisions about who comes into MIQ. Our job is to look after them once they are with us."
Main said if the crew from Playa Zahara were assigned to MIQ, they would most likely go to the Sudima Christchurch Airport Hotel.
She said all MIQ facilities operated at an alert level 4 environment.
Main would not say if the demands on MIQ increased as a result of the fishing crew having to be cared for.
"MIQ is here to look after people coming to New Zealand with or without Covid that need to go through our facilities."
The Sudima Christchurch has negative pressure rooms and a dedicated quarantine wing.
Five of the crew are considered to be at the end of their infections and will remain onboard to maintain the safety of the vessel, the Ministry of Health spokesperson said.
The crew arrived in New Zealand on June 18 and spent two days at a managed isolation facility in Auckland.
The Playa Zahara was near the coast of Kaikōura at about 8am on Friday.
"The transport of the 13 crew to the quarantine facility will be done using standard Infection Prevention and Control (IPC) protocols, including the use of appropriate PPE.
"IPC protocols will also be adhered to for the ship while it is docked at the port."
The timing of the ship's arrival to Christchurch is dependant on the weather and boat speed. RNZ has reported it is due to arrive in Lyttelton tomorrow.
Swabs of the crew were taken in Port Taranaki on Tuesday after reports of a flu-like illness on board.
The ship is not affiliated with the New Zealand fishing industry.
It is the second fishing vessel in New Zealand waters dealing with a Covid-19 outbreak.
A fairer MIQ booking system in the works
As travellers find it harder to secure a managed isolation rooms, it has come to light that some tech-savvy people are able to game the system.
"The reality is some people will miss out," Main said.
However, there was an emergency allocation process and not everybody qualified for it, she said.
"MIQ has been a great success. We've got great freedoms in New Zealand that MIQ is part of enabling."
Main said steps would be taken to make it easier to get through the booking system quickly.
"There's been a lot of discussion about bots, these scripts that can help people to refresh the page quickly to check dates, to fill in forms," she said.
"In the next few days, we'll be making a change to make it more fair, so that you don't need to repopulate the fields when you refresh the page. So that takes quite a step out of the booking process.
"We added recaptchas, which is where you click those little images to make it fairer to make sure that those scripts don't go through with the booking."
"But ultimately, when we've got more people wanting to come than we've got space it's going to be difficult."
-RNZ and NZ Herald
