The Brazil forward, 19, is expected to be out for two to three months after breaking a metatarsal during Monday’s 2-0 Premier League victory at Bournemouth.
He had an operation in Barcelona on Thursday, and is expected to spend some of his recovery time back home in Sao Paulo.
Jesus, who completed a £27m move from Palmeiras in January, had been in superb form, scoring in each of his first two league starts, against West Ham and Swansea.
City are hopeful that the striker might yet be back in action before the end of the campaign, but Guardiola has made clear that he will not rush the forward back.
The City manager said: “So last night, there was an operation. It was good, really good. The important thing is a good recovery. He’s coming back when he is fit. I don’t know if it will be the end of this season or next season. Now we’re giving all our support to him and his family and waiting for him to come back.”
Asked if that meant there was a chance that Guardiola would not be back this season, Guardiola added: “I don’t know. His recovery is between two and three months.”
Jesus’ injury means that Sergio Aguero is set to be pushed into the central attacking role when City host Monaco in the first leg of their Champions League last-16 tie on Tuesday. Aguero has been left out of the starting line-up for City’s last three league matches, which has cast doubt on his long-term future at the club, even though he has a contract until 2020.
Guardiola said a week ago that he wanted the Argentina international to stay, but also indicated there was no guarantee that would happen. The City manager has been impressed with the way that Aguero has pushed to get back into the starting line-up since being dropped.
“From the beginning of the season, not just in these three games, Sergio has always played more than well. Not just Sergio, all the players,” Guardiola said. “It’s not easy for the players who don’t play, and have been out of the team for a long, long time in many cases, like Kelechi Iheanacho. Being more than professional is impossible, so it was perfect – Sergio did that.
“He showed that when he came on against Swansea, or against Bournemouth after the injury to Gabriel. He came in and played well, and was involved in the second goal. I don’t have doubts about his quality, because it was always there.
“Sergio has to do what he has done all his career, nothing more. What I ask of Gabriel Jesus, I am not asking of central defenders, or Iheanacho or the wingers. Every player has his own quality, and has to show that.”
Before the Monaco match, City travel to Championship promotion contenders Huddersfield in the fifth round of the FA Cup on Saturday. Guardiola is expected to rest several key players to keep them fresh for Champions League action, but remained quiet on whether Claudio Bravo might get a recall in goal.
Bravo was dropped in favour of Willy Caballero last month after a poor run of form, but asked who would be his goalkeeper at the John Smith’s Stadium, the manager said: “I am going to decide tomorrow.”Reuse content