City said that neither forward Mahrez nor defender Laporte, now self-isolating, were displaying symptoms.
It comes just days before the Premier League season starts on September 12.
A club statement released on Monday morning said: “Manchester City FC can confirm that Riyad Mahrez and Aymeric Laporte have tested positive for Covid-19.
“Both players are currently observing a period of self-isolation in accordance with Premier League and UK Government protocol on quarantine. Neither is displaying symptoms of the virus.
“Everyone at the club wishes Riyad and Aymeric a speedy recovery ahead of their return to training and the new season.”
Mahrez, tweeting in response to messages of support from City fans, said: “Thank you for all the nice messages, I’m good. Stay safe everyone take care of you.”
City’s first fixture of the new Premier League season is on September 21 when they face Wolves at Molineux.
City will also begin their Carabao Cup defence later that week. They will face either Bournemouth or Crystal Palace in a third round tie.