Oscar-winning actor Tom Hanks and his wife, actress Rita Wilson, have tested positive for coronavirus in Australia, the actor said on Twitter.

Hanks said he and Wilson, both 63, were tested in Australia, where he is working on a film after they felt tired and achy with slight fevers.

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"To play things right, as is needed in the world right now, we were tested for the coronavirus and were found to be positive," Hanks said in the tweet.

The film star said he and Wilson would be "tested, observed and isolated" for as long as required.

The couple are the first major US celebrities known to have contracted COVID-19. The coronavirus has infected more than 1,000 people in the US.

"Not much more to it than a one-day-at-a-time approach, no? We'll keep the world posted and updated," Hanks tweeted.

Hanks had travelled to Australia to begin filming an upcoming movie about Elvis Presley. He is set to play Presley's manager, Colonel Tom Parker, in the Warner Bros production.

"We have been made aware that a company member from our Elvis feature film, which is currently in pre-production in The Gold Coast, Australia, has tested positive for COVID-19," Warner Bros said in a statement.

"We are working closely with the appropriate Australian health agencies to identify and contact anyone who may have come in direct contact with the individual.

"The health and safety of our company members is always our top priority, and we are taking precautions to protect everyone who works on our productions around the world," the studio said.

The Warner Bros statement did not mention Hanks.

The actor is staying on the Gold Coast, in eastern Australia, which has one of the country's main Hollywood studios and where filming was to take place.

"The Elvis biopic filming has been closed down. I understand it will be 14 days quarantine and testing ... our heart goes out to Tom and his wife," Tom Tate, mayor of the Gold Coast, said in a press conference.

The couple's son Chet took to Instagram to say he had spoken with his parents on the phone and that both were fine and there was no cause for major concern.

"Yeah, it's true, my parents got coronavirus. Crazy," he said in a video message. "They're not even that sick. They're not worried about it, they're not trippin', but they're going through the necessary health precautions obviously."

Wilson appeared on Monday on a chat show on free-to-air broadcaster Nine Entertainment Co Holdings Ltd. The network said employees who had been in contact with her would be tested for the coronavirus and quarantined for 14 days.

Hanks won the Academy Award for best actor for his role in 1994's Philadelphia, in which he plays a man stricken with AIDS, and Forrest Gump the following year. Wilson has appeared in such films as Sleepless in Seattle and Runaway Bride.

The coronavirus has infected more than 121,000 people in 118 countries while over 4,300 people have died due to the virus, a Reuters tally shows.

In the US, at least 37 people have died from the respiratory illness.