The Oscar-winning actor, 63, has been in Australia filming an upcoming Elvis Presley biopic and said he started experiencing symptoms of the virus.
Hanks said he felt like he had a cold, while Wilson, also 63, suffered from chills.
They have both tested positive for coronavirus, Hanks said on Instagram.
In a statement, he added: "Well, now. What to do next? The Medical Officials have protocols that must be followed. We Hanks' will be tested, observed, and isolated for as long as public health and safety requires. Not much more to it than a one-day-at-a-time approach, no?
"We'll keep the world posted and updated. Take care of yourselves!"
Hanks, a two-time Oscar winner and star of films including Forrest Gump, Saving Private Ryan and The Post, is the highest profile Hollywood figure to be diagnosed with the Covid-19 virus, which is sweeping the world.
Moments before Hanks posted to Instagram, Donald Trump addressed the US and announced a host of new measures, notably suspending all travel from Europe, excluding the UK, for 30 days starting from Friday.
Hanks and Wilson's son, Chet, 29, assured fans his parents were fine. In an Instagram video, he said: "Yeah, it's true. My parents got Coronavirus. Crazy. They're both down in Australia right now because my dad was shooting a movie down there but I just got off the phone with them. They both are fine, they're not even that sick."
He said neither of the actors is worried about the illness, but are taking the necessary precautions.
"But I don't think it's anything to be too worried about," Chet added. "I appreciate everyone's concern and the well wishes but I think it's all going to be alright but I appreciate it and just, everybody stay safe out there. Much love."
The entertainment industry is also reeling from the outbreak and a host of major events have been cancelled.Hanks is starring as Presley's longtime manager Colonel Tom Parker in the biopic, while US actor Austin Butler will star as the singer.
In a statement to Deadline, Warner Bros said: "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 (coronavirus).
"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 World Health Organisation has declared the coronavirus a pandemic.
As of Wednesday, there were 460 confirmed cases in the UK and eight people had died after contracting the disease.