Sinclair, 24, did not travel with Roberto Mancini's squad to face his former club Swansea after being taken ill during training on Friday.
Sinclair is understood to be in a comfortable condition and his illness is not life-threatening.
The club tweeted a get-well message to the former England Under-21 international, and manager Roberto Mancini said: "Scott had a problem yesterday, I don't think it is a bad situation and it is under control."
Press Association Sport understands Sinclair in being treated at the Alexandra Hospital in Manchester and the club expect to know more about his condition within the next 48 hours.
Sinclair would now appear unlikely to have any hope of playing a part in next Saturday's FA Cup final against Wigan at Wembley at the end of a frustrating first season with the club.
Since leaving Swansea for the Etihad Stadium he has made just two Premier League starts, and reports claim Mancini is willing to listen to offers for the ex-Chelsea player.