Fernandinho came on as a substitute during the UEFA Champions League clash against FC Porto, but managed to play only four minutes.
Gabriel Jesus and Benjamin Mendy are also sidelined for a period of time for Manchester City, who on Thursday, welcomed Kevin de Bruyne and Aymeric Laporte back to training.
"It is bad news," Manchester City boss Pep Guardiola was quoted as saying by ESPN.
"It will be four to six weeks out. With this amount of games we need people here but it is what it is."
Nathan Ake, too, didn't play the game against Porto, but Guardiola was hopeful that the Dutchman's absence was only precautionary, and not indicative of a bigger injury, like Jesus's or Mendy's.
Only last week, Manchester City welcomed Sergio Aguero back into the first-team fold, when the Argentine started the 1-0 win over Arsenal in the Premier League.
Manchester City face injury crisis with mounting fixture list
Guardiola's concerns over the fitness of his players come amidst a period when Manchester City play once in three days every week, as the Cityzens juggle Premier League and Champions League international break.
Before the next international break, Manchester City face West Ham, Marseille, Sheffield United, Olympiakos and Liverpool.
"We'll start with Kevin and Laporte training but I don't know how they'll come back," Guardiola said.
"We get players back and others we lose. In three days we go to London and then to France to play Marseille and then Sheffield. It's so demanding and we need all the players back."
In addition to the injury crisis, Guardiola also spoke about the future of Eric Garcia, who has been linked with a move back to his native Barcelona.
Garcia's contract expires at the end of the season, and he has made it clear that he would want to go back to Barcelona. But Guardiola has not ruled out the possibility of convincing the young Spaniard to sign a new contract at Manchester City.
"I know he wanted to leave, maybe we can seduce him to extend with us," Guardiola said.
"He's a guy who is so stable in many things and we are so happy to have him here."Published 23 Oct 2020, 12:16 IST