"I'm not going to take any chances on this issue", Mr McGowan told reporters on Wednesday.
The only exception, he said, would be a life-threatening emergency. There are 950 passengers and 550 crew in total, including 109 New Zealanders and 33 from Britain.
Any visitors on the island have been ordered off the island so it can be prepared as a quarantine base.
For those who were keeping track of the news, you may probably have caught wind of the Diamond Princess cruise ship at some point, as for a period of time, the cruise ship suffered from an outbreak of the Covid-19 virus on-board, forcing passengers and crew to be trapped in isolation.
Despite assurances from Vice-President Mike Pence and California Gov. Gavin Newsom that everyone aboard the ship would be tested for the novel coronavirus after the ship docked, only 1,100 passengers of about 2,400 have been tested, Kelly said.
San Francisco resident Lyn Hamilton was also quarantined at Travis AFB along with her husband before being released on Tuesday after showing no symptoms for 14 days.
The country is taking strict precautionary measures with arriving cruise ships after one liner, the Ruby Princess, disembarked in the country with minimal health screening.
The Canadian government has advised against cruise ship travel until further notice.
The Princess Cruises ship, carrying 3 700 passengers and crew, was quarantined on 5 February by Japanese officials in the port of Yokohama after Covid-19 was detected.
The Artana, with 1,300 people on board, has also been asked to remain at anchor off the coast, McGowan said.
Police, local government and Aboriginal patrols will monitor for breaches.
OPINION: Is this Morrison and McGowan government's Tampa moment? All overnight visits, day trips and visits by private and commercial vessels have been banned indefinitely, according to the Rottnest Island Authority's website.
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". The ship is now carrying 950 passengers and 550 crew, with 800 Australian nationals on board.
"Two thirds of cases we now have are from an Australian who has come home from overseas, that is very different to what we're seeing in rest of the world", Mr Morrison said.