"After a close contact, I've been self-isolating and the latest test I took was positive for COVID 19," he said on Twitter. "I had some symptoms and I'm following doctor's orders for recovery. Take care, everyone!"
Aguero, City's record scorer, has missed their last four games, including Wednesday's victory over Aston Villa.
"We need Aguero, we miss him. The numbers speak for themselves, the best striker in our history," manager Pep Guardiola said ahead of the Villa game.
City face fourth-tier Cheltenham Town in the FA Cup fourth round this weekend.