"After a few days of self-quarantine, and not feeling great, I have tested positive for coronavirus," Cohen said in Friday's post.
"As much as I felt like I could push through whatever I was feeling to do #WWHL from home, we're putting a pin in that for now so I can focus on getting better. I want to thank all the medical professionals who are working tirelessly for all of us, and urge everybody to stay home and take care of themselves."
The 51-year-old television personality also shared a photo of him sitting on the couch, with an unshaven face and wearing a terry cloth sweatshirt.
EW.com said Bravo had previously announced Cohen's show would be taped at his New York City apartment with celebrity guests appearing via video chat.
Other well-known entertainment figures who have tested positive for the virus include Hollywood couple Tom Hanks and Rita Wilson, Luther star Idris Elba, Lost alum Daniel Dae Kim and former Game of Thrones cast-mates Indira Varma and Kristofer Hivju.