There are now 128 people with Covid-19 on Aurora Expeditions’ Greg Mortimer, which set off on an Antarctica and South Georgia voyage on 15 March.
That is 58% of everyone onboard the ship, which is now stranded off Uruguay.
Guests from Australia and New Zealand will fly to Australia for their two-week quarantine on a chartered flight which is carrying the "hard cost" of AU$15,000 per person.
This price includes the flight from Portugal to Uruguay, then to Australia and back to Europe, as well as extensive cleaning and two flight crews.
Aurora said it has asked the Australian government for support to cover the ticket price.
European and American passengers with Covid-19 must wait onboard the ship until they have a negative test result.
A spokesperson from Aurora said: "Accordingly, we will be organising a new swab for all positive passengers in the coming two days.
"We expect as passengers test negative we will then be able to organise their departure. We have notified our passengers’ respective embassies.
"Ideally, we hope that these passengers will be allowed to finish their quarantine onshore once the Australians and New Zealanders are off the vessel."
