"Rita and I are down here in Australia," he said in a statement. "We felt a bit tired, like we had colds and some body aches. Rita had some chills that came and went. Slight fevers, too. To play things right, as is needed in the world right now, we were tested for the coronavirus, and were found to be positive."
He said they will follow the protocols set out by medical officials.
"We Hanks will be tested, observed and isolated for as long as public health and safety requires," he added. "Not much more to it than a one-day-at-a-time approach, no?"
The statement accompanied a photo of a rubber glove in a trash can lined with a hazardous materials garbage bag.
"We'll keep the world posted and updated," he said. "Take care of yourselves!"
Hanks has been cast as Col. Tom Parker in the Lurmann film along with Austin Butler, who is to play Elvis, and Maggie Gyllenhaal in the role of Gladys Presley, Elvis' mother.
The virus, which first emerged in Wuhan, China, in December, has since traveled the world over, infecting more than 120,000 people. More than 4,600 people have died due to the virus, according to a live tally by Johns Hopkins University.