Instead, McGowan said, the 800 Australians onboard, including 250 people from WA, will be made to complete a mandatory 14-day quarantine period on Rottnest Island in an effort to prevent a potential coronavirus outbreak from spreading to the general population.
Two vessels carrying global passengers have been denied access to berth at a local port, and are now stationed off the coast of WA.
The ship's operator, Cruise and Maritime Voyages Australia, said it was disappointed it was not told that its docking permission had been rescinded before McGowan announced it to the media.
The Magnifica departed after refuelling at Fremantle but was forced to turn back when Dubai refused to allow it to dock.
"The Artania cruise ship must continue on its journey to South Africa urgently", he said.
"There are no circumstances where we will allow passengers or crew to wander the streets in our state".
Mr McGowan said he thought Garden Island would be a suitable place to put sick passengers from the Artania who needed to go to shore for treatment.
The MSC Magnifica is believed to be carrying 1,700 European nationals, with no Australians on board.
"We have seen what has happened in Sydney Harbour", McGowan told reporters in Perth on Wednesday.
Vulnerable people and those in high risk settings such as aged care, Aboriginal communities, detention centres, boarding schools and military barracks will be tested if there are two or more people with respiratory illness.
One passenger, no longer on board the ship, has tested positive for COVID-19.
Another cruise ship, the Artana, was due to refuel in Fremantle on Tuesday night.
"The chief health officer of this state ... said they can be treated on board".
The Vasco da Gama cruise ship is scheduled to dock on Friday and the 800 Australians will be transferred to Rottnest Island for self-isolation.
Among those on board, around 800 are Australians, including 200 Western Australians. About 109 passengers are from New Zealand and 33 from the United Kingdom.
In the last two days Rottnest Island has been cleared of visitors and accommodation, catering, and security has been organised.
He said: "All crew and foreign nationals will remain on the ship until arrangements are made to fly them directly out of the country".
"No one will be allowed to disembark unless a passenger is in a life-threatening emergency, where they will receive medical attention".
The WA Government has said it is in consultation with New Zealand to arrange a repatriation flight as soon as possible.
The Tourism Minister for WA Paul Papalia, said that "The intention is that we take people out there who are well, they isolate for 14 days, hopefully they come off at the end of that time and they can go back home".