Hanks and Wilson, both 63, sought medical advice after experiencing the symptoms of a cold in Queensland, the actor wrote on Instagram.
They will now spend time in isolation, he added.
The US couple were on the Gold Coast as Hanks worked on Baz Luhrmann's new film about the life of Elvis Presley.
On Wednesday, the World Health Organization (WHO) officially declared the outbreak to be a pandemic.
Hanks wrote on Instagram: "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".