The Viking Bay, a deep-sea fishing vessel carrying two Covid-infected mariners, has docked at Queens Wharf in Wellington.
Crew on board can be seen wearing masks.
As it is now a quarantined vessel, perimeter fencing has been put around the ship and maritime security and police are monitoring the wharf and the water. Media and the public are asked to avoid the area and to respect the privacy of the crew.
"A mobile health unit has been set up. The crew will disembark later today and be tested," the ministry said in a statement.
Seven of the 20 crew will remain aboard to meet maritime safety requirements. The remaining 13 crew – which includes the two crew who last week tested positive – will be transferred to a Wellington quarantine facility. Infection prevention and control protocols will be in effect, including use of PPE.
"The risk assessment has been reviewed and this situation remains to be considered a low risk to public health."
There are no new cases of Covid-19 to report in the community. There is one new MIQ case, who arrived from the Netherlands via Singapore, on July 9.
Customs' group manager maritime Stephen Waugh has said there is very low public health risk.
"The crew will be transported at a time that will minimise the risk of coming into contact with members of the public.
"Customs will maintain presence at the port throughout the operation, with the support of additional security personnel, and the Police Maritime Unit maintaining watch over the water."
Customs said all Government and CentrePort staff who interact with the vessel or crew are vaccinated.
Shipping vessel applies for crew change in Taranaki
Meanwhile Spanish-flagged shipping vessel the Playa Zahara, which has had reports of a flu-like illness on board, has applied for permission for a change of crew at Port Taranaki.
Health authorities will provide testing for crew members on the ship shortly after it berths tomorrow.
The ship will then depart from the onshore quarantine place of inspection and will remain offshore until test results are available on Thursday.
"If the results show there is no evidence of Covid-19 onboard, then the vessel will be granted pratique for a crew change. Health authorities have assessed this situation as having a low risk to public health," the ministry said.
Green zone flights resume from Queensland
Officials confirmed that quarantine-free flights from Queensland to New Zealand can resume from 11.59pm tonight. The public health risk is regarded as low.
Travellers will need to have returned a negative pre-departure test and complete a travel declaration.
Meanwhile, the emergency Air NZ "green flights" from New South Wales over the next two weeks have all sold out.
They went on sale this morning at 10am and were snapped up immediately.
Only 40 to 60 seats were made available on each flight on a first-in, first-served basis.
The emergency flights have been put on for New Zealanders who are stranded in the Australian state because of the latest Covid-19 outbreak there.
Those travellers will not need a pre-departure test.
Travellers who have been in NSW on or after 10.30pm on June 26 are not permitted to travel back to New Zealand from other parts of Australia. Travel histories will be checked at the airport before flying.
Anyone wanting to be granted a trip home on compassionate or urgent grounds can call (04) 439 8235 from 10am to 10pm (NZT) Monday to Friday. People can also send an email via NSW2NZ@mfat.govt.nz.
They will need to meet eligibility requirements, such as there being a serious health or safety risk that means they need to return to New Zealand as soon as possible.
Leanne Geraghty, of Air New Zealand, said: "We would love to be able to bring more Kiwis home to their families, but we're limited by the availability of [managed isolation and quarantine] spots."
Those trying to get home on any of these flights do not have to search for an MIQ spot separately, because each seat will be linked to an available room in an MIQ facility.
About 20 per cent of all MIQ spots are being set aside for those wanting to get home urgently on compassionate grounds. Those are being managed by government officials, the airline said.
The first green flights from NSW are scheduled to touch down tomorrow at 2.25pm in Auckland and 11.55pm in Christchurch, respectively.
The next flights throughout the week are scheduled to arrive in Auckland, while one will land in Christchurch on July 23.