Kvaratskhelia twisted his knee during PSG's 4-2 win on Tuesday and was helped off the pitch just before the hour mark, with the Georgian winger unable to put any weight on his leg.
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Meanwhile, Ousmane Dembele was also forced to come off in the 19th minute due to a thigh injury, while defender Marquinhos was substituted with a similar injury.
PSG said both players will remain under treatment for the next few weeks.
PSG are top of the standings in the Champions League with three wins from three games.