Wilson, who is 72, was tested Monday morning, and his results came back positive Wednesday.
Wilson said he was in Danville, Illinois, Saturday for a campaign event and began feeling sick Sunday night.
He was handing out gift cards during a drive-up event at a church, he said.
He also had two public events Sunday, including one at a Northwest Side church. But Wilson said he had no idea at the time that he had the virus, or he never would have been in public.
"It's real, so don't think it's not real," Wilson said.
During the service at Storehouse Church, Wilson was singing with other people standing near him without masks or social distancing.
He is home in south suburban Hazelcrest self-isolating and checking in regularly with his doctor. He said he has mild symptoms and is suspending all in-person campaigning for the next 10 days.
"Like so many of my fellow Americans, I am not immune from COVID-19," Wilson said in a statement.
RELATED: Illinois Election 2020: Meet the Candidates
He said he is experiencing body aches and some wooziness, and his driver and media representative have also tested positive for COVID-19.
Wilson, a philanthropist and perennial candidate, has given away 27 million masks, and takes safety seriously at his events, he said.
"And we usually don't wear it when we get ready to speak, but we wear masks, wear gloves; we follow all the protocols and things of that nature," Wilson said.
Mayor Lori Lightfoot is among those wishing him well.
"Dr. Wilson has a very generous heart. He's contributed mightily in a lot of different causes, and, particularly, supporting Black churches on the South Side and West Side. And I wish him well and a speedy recovery," she said.
Wilson is running against incumbent Sen. Dick Durbin, a Democrat; Mark Curran Jr., a Republican; David Black, a Green Party member; and Danny Malouf, a Libertarian, in the 2020 November election.
Wilson is running as a member of the "Willie Wilson Party" and an Independent. He has also run for president in the past.
He plans to campaign virtually while he is recovering and will get back on the campaign trail as soon as his doctor tells him it's safe to do so.