About 800 of the passengers are Australian and will be taken to nearby Rottnest Island for a 14-day quarantine period, Western Australian Premier Mark McGowan told reporters.
The outbreak from the Ruby Princess represents the country's worst cluster of the virus and has sparked anger over why passengers, more than a dozen showing flu-like symptoms, were cleared to disembark without basic health checks.
The Diamond Princess, a cruise ship that captured headlines after an outbreak of COVID-19 among those on board, left a pier in Yokohama port Wednesday after almost two months of quarantine.
It comes after the NSW government faced heavy criticism for allowing thousands of passengers from the Ruby Princess ship to disembark in Sydney Harbour last Thursday.
There was little health authorities could do to prevent the disembarkation of asymptomatic cruise passengers, she said on Wednesday.
Western Australia is preparing Rottnest island, a former prison island turned tourist attraction, to quarantine some of the 800 Australians on board a third cruise ship, the British-operated Vasco de Gama.
"The Magnifica and Artania both need to leave and go back to their port of origin and leave as soon as possible", said McGowan.
Cruise ships have become a flashpoint after 147 of the 2,700 passengers allowed to disembark from Carnival Corp's Ruby Princess later tested positive for the virus, a blunder that underlined official tensions in handling the crisis.
The state has blocked two further cruise ships, the Magnifica and Artania which, according to the ABC, have no Australian nationals on board.
A second cruise ship, the MSC Magnifica, which refuelled in Perth this week, is now in Western Australian waters after being refused entry in Dubai.
Shipowner Britain's Cruise & Maritime Voyages said it was carrying no unwell passengers or staff.
More research must be completed to determine if virus can be transmitted by SARS-CoV-2 fomites (objects or materials which are likely to carry infection, such as clothes, utensils, and furniture), the company said, in a statement. More than 100 other passengers, from Britain and New Zealand, will be quarantined on the ship.
DFAT "continues to work closely with the cruise industry and cruise line operators to provide advice to Australian passengers on cruise ships with itineraries impacted by COVID-19", a spokesperson said.