Sinclair did not travel with Roberto Mancini's squad to face his former club Swansea after being taken ill during training on Friday but is understood to be in a comfortable condition.
The club confirmed the news on Twitter, and Mancini, speaking after the goalless draw in Wales, said: "Scott had a problem (on Friday). I don't think it is a bad situation and it is under control."
City expect to know more within 48 hours but the 24-year-old would 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.
He moved to Manchester from the Liberty Stadium last summer but has made only two Premier League starts.