The 21-year-old French midfielder, who joined from Lyon in the summer for around 25 million pounds, has picked up an injury and missed Sunday's 2-1 defeat away to Brighton.
Erling Haaland had given City the lead at the Amex Stadium, but two second-half goals from the hosts secured the points.
Guardiola admitted the news on Cherki was a serious concern. "He's out for two months. Seven or eight weeks," the City manager told the club's website.
Cherki's lay-off leaves Guardiola with fewer creative options in midfield ahead of a busy September, which includes a Champions League group opener and the derby against Manchester United on 14 September at the Etihad Stadium.
Cherki had shown flashes of quality in pre-season and was expected to play a key role in linking City's midfield and attack.
The Brighton match also brought another worry as January signing Abdukodir Khusanov was forced off with a knock.
The 20-year-old Uzbekistan defender made his first start of the season and earned praise from Guardiola before his early withdrawal. "He did very well until the injury. We will see what the doctors say," Guardiola added.
City have already lost ground in the Premier League title race after two defeats in their opening fixtures, and Guardiola admitted that younger players could now be asked to step up. "We have to adapt. Other players will get opportunities," he said.