The Brazilian forward suffered the knock during training and is not expected to return until after the international break, the club revealed ahead of Sunday's encounter at Bournemouth.
The injury will rule Jesus out of City's next fixture against Brighton and Hove Albion.
The 22-year-old has dealt with a number of injuries since his arrival at City in 2017. He was limited to just 29 appearances last season.
Jesus started the season on a positive note after finding the back of the net in City's 5-0 thrashing of West Ham United on the opening day of the season.