Southern DHB health officials were working with other agencies to determine the next steps for the ship.
In the meantime, the crew members would remain on board the Mattina.
The ship is currently in quarantine in a secure area of the port in Bluff which cannot be accessed by members of the public.
Fencing would be put up to further restrict access to the vessel.
Two other ships in New Zealand waters have also been faced with recent Covid-19 outbreaks.
Eighteen crew members of the deep-sea fishing vessel Viking Bay have tested positive for Covid-19, while vessel Playa Zahara has 16 positive cases among its 18 crew members, the ministry said.
There were no Covid-19 cases reported in the New Zealand community today, and three positive cases in MIQ.