Sheeran, 30, broke the news on social media days before his new studio album is due out.
"Quick note to tell you that I've sadly tested positive for Covid, so I'm now self-isolating and following government guidelines," Sheeran wrote on Instagram.
"It means that I'm now unable to plough ahead with any in person commitments for now, so I'll be doing as many of my planned interviews/performances I can from my house. Apologies to anyone I've let down."
Representatives did not immediately say which performances he is canceling and which he will carry out from home.
Sheeran's official website lists no performances before April.
The four-time Grammy winner's new studio album is called "=" which is pronounced "Equals".