According to L’Équipe, the 19-year-old was forced off just 12 minutes into Tuesday’s 2-0 victory over Estonia following a challenge from an opponent.
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France U21 coach Gerald Baticle admitted afterwards that he was concerned about the injury.
Should the three-week recovery timeframe be confirmed, Mbappe would miss Lille’s Ligue 1 fixtures against Le Havre on October 10 and Stade Brestois 29 the following week.
The youngster has made six appearances this season, starting five, while contributing one goal and one assist.
Mbappe is already suspended for three Champions League matches following his red card against Real Betis, meaning he would have missed Lille’s high-profile encounters with Arsenal and Galatasaray regardless of the injury.