Sixteen of the 18 crew of the Spanish-flagged shipping vessel the Playa Zahara have tested positive.
The swabs were taken in Port Taranaki on Tuesday after reports of a flu-like illness on board.
The vessel had requested access to the port for a scheduled crew change.
Standard Infection Prevention and Control (IPC) protocol, including the appropriate use of PPE, was used throughout the crew's testing.
After the tests were taken, the ship again departed from Port Taranaki and is now on its way to Lyttelton where the appropriate level of support can be provided.
"Health authorities are working on arrangements for the crew once they arrive at Lyttelton Port," the Ministry of Health said.
"This includes whether they quarantine aboard the ship or are transferred to a quarantine facility on shore. If any confirmed cases are to be transferred, that will also be done using standard IPC protocol."
The Playa Zahara's shipping agent and its crew are cooperating with officials.
Whole genome sequencing is underway.
Spokespeople for the ports of Taranaki and Lyttleton referred the Herald to NZ Customs, which have been approached for comment.
No Port Taranaki staff members would be in contact with those on board the vessel either, he said then.
"Should any crew members return a positive Covid-19 test result, we expect the vessel will head to a port where there are managed isolation facilities close by, as has occurred with the Viking Bay."
The Viking Bay was the vessel that first reported a Covid case among its crew; with two mariners confirmed as having Covid-19 last week.
Earlier this week, a further 13 crew members tested positive as well. Both fishing vessels are Spanish-flagged.
All those affected have been transferred to an on-shore managed isolation facility in Wellington.
