The City winger had the surgery on Saturday and Mancini has said that the situation is being dealt with effectively by the staff at the Alexandra Hospital in Manchester.
"Scott had a problem yesterday, I don't think it is a bad situation and it is under control," he said.
Sinclair's condition had previously been described as "not life-threatening", with
the club's official Twitter account sending the player a get well message on Tuesday.
"Get well soon Scott Sinclair from everyone at Manchester City FC #MCFC," read the tweet.
The former Swansea City winger has made just two Premier League starts since his move to the Etihad last summer.