The Arsenal centre-back was injured in an unsuccessful attempt to prevent Alvaro Negredo from scoring in their Premier League clash on Saturday, Thomas Vermaelen replacing him
The Frenchman suffered the injury in a challenge with Alvaro Negredo in the 39th minute, but it ended unsuccessfully for the Gunners as the striker put Manuel Pellegrini's side 2-1 ahead.
"He has a cut and he will be out for a while but for how long I don't know," Arsenal manager Arsene Wenger said after the match.
Despite a double from Theo Walcott and Per Mertesacker's late effort, Arsenal slipped to the heavy defeat following two strikes from Fernandinho, as well as goals from Sergio Aguero, Negredo and a penalty from Yaya Toure.
Arsenal's lead at the top of the Premier League has now been cut to two points following Chelsea's 2-1 win over Crystal Palace.
It was Koscielny's 21st appearance of the season for the league leaders but he may face long wait for his next, with Thomas Vermaelen introduced in his place at the Etihad Stadium.
Koscielny's partnership with Per Mertesacker has helped Arsene Wenger's side into the knockout stages of the Champions League this term.
He also played his part in the France national team's qualification for World Cup 2014.