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.
Five crew are considered to be at the end of their infections and will remain onboard to maintain the safety of the vessel, the spokesperson said.
The crew arrived in New Zealand on June 18 and spent two days at a managed isolation facility in Auckland.
They provided negative pre-departure tests before arriving in New Zealand and tested negative before boarding the ship, they said.
The Playa Zahara was near the coast of Kaikōura at about 8am on Friday morning.
"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 things such as weather and speed but an estimated time would not be provided for security reasons.
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.
