The 19-year-old forward started the match ahead of Sergio Aguero but limped off after just 15 minutes and underwent tests on Tuesday morning.
The Brazilian will undergo further examinations in the coming days to establish the extent of the injury, but it is feared he could be out of action for three months.
Jesus has made an immediate impact at City after joining the club in £27million deal from Palmeiras in January.
He has scored three goals in his five appearances, including an injury-time winner against Swansea, and so impressive were his performances he was being selected ahead of top scorer Aguero.
That situation had sparked fresh speculation over the future of Aguero, who has scored 154 goals for City since joining the club in 2011.
Aguero, 28, replaced Jesus at the Vitality Stadium and forced the Tyrone Mings own goal which saw City complete their 2-0 victory and move to second in the Premier League.
The Argentina international is now likely to continue leading the line, although City are not in Premier League action again until March 5. They travel to Huddersfield in the fifth round of the FA Cup this weekend.