The 20-year-old Brazilian striker went off in tears during the first half of Sunday’s 0-0 draw at Crystal Palace.
And Guardiola confirmed the expected length of his lay-off after Tuesday’s 3-1 home victory over Watford.
The Spaniard said: “He will be out between four and six weeks – a little bit longer, I don’t know – but between one month and two months.”
Jesus, who has a medial collateral ligament injury, was at Etihad Stadium to watch the match against Watford.
Guardiola was boosted by having playmaker Kevin de Bruyne fit to start against the Hornets after he had left the field on a stretcher on Sunday.
But the City boss must now wait for news on the fitness of full-back Kyle Walker, while doubts remain over playmaker David Silva’s future availability.
Walker pulled up at the end of the win over Watford with an apparent groin injury, and Guardiola said: “We are going to check it out.”
Silva, meanwhile, returned to the side on Tuesday having missed recent games for personal reasons.
Guardiola said: “We are very happy David Silva is back with us. We don’t know how long he will be with us but you saw again he is an essential player with us. He wants to stay but family is the most important thing.”
Tuesday’s victory sent City 15 points clear at the top as they showed no ill-effects from the end of their 18-game Premier League winning run at Palace.
But Guardiola warned the festive period is “going to kill the players” after his side played their 10th game in a month.