Eight New Zealand passengers were set to be on the Australia-assisted evacuation flight, but two have since tested positive for the Covid-19 coronavirus.
They were barred from taking the evacuation flight, which left Tokyo at 5am.
The Ministry of Foreign Affairs and Trade said during final medical checks, two of those passengers tested positive for Covid-19 and did not travel on that flight.
They are being treated in hospital in Japan and Mfat consular staff remain in contact with them.
The remaining six passengers are scheduled to land in Darwin about midday today (NZ time), before being transferred to a New Zealand Government-chartered flight - a 13-seat Bombardier Global Express Aircraft - scheduled to land at Whenuapai about 7pm.
The passengers will be tested by the Australian Medical Assistance Team twice on the flight to Darwin, and again on the ground in Darwin.
Passengers with any symptoms will be taken into the Australian hospital system in the Northern Territory city.
On arrival in Darwin, an Mfat official will facilitate the transfer of passengers who have passed the screenings to the charter plane.
A St John paramedic will join the charter flight to Auckland and a doctor will also be on board.
Upon arrival at Whenuapai, passengers will be transferred to Whangaparaoa to begin their 14-day quarantine.
It was reported yesterday that 88 people on the ship had tested positive for coronavirus, taking the total number of those infected to 542.
There were originally 3700 people on board the ship when it docked in Yokohama on February 4.
Japanese health officials said 65 of those who had been recently confirmed as infected were not showing any symptoms.
The 14-day quarantine period for the ship ends today, and passengers have been told if they test negative they will be able to leave.
Many countries have already made arrangements to get their citizens home. On Monday, the US evacuated 330 Americans who had been on board the ship, while 11 New Zealanders remained on board.
Aside form the six heading home and two hospitalised in Japan, another two Kiwis have chosen to stay offshore for another 14 days before returning to New Zealand, while the third is an overseas resident, according to a spokesman from the office of Minister of Health David Clark.
The New Zealand passengers have been asked to contribute a fee of $500 to cover the costs of the assisted departure.
