Graham was forced off after just 16 minutes of the game at Goodison Park after coming off worse in a challenge with Gareth Barry.
Scans revealed no serious problem but he is likely to miss City's back-to back games with Tottenham in the Premier League and Capital One Cup.
The 28-year-old will also sit out the league game with his former club Sunderland at the KC Stadium on 2 November but could be fit to return for the trip to Southampton a week later.