The 20-year-old forward returned from a hamstring problem in the 1-0 win over Bordeaux on September 28 but suffered a complication to the treated area, leading him to miss the 4-0 Ligue 1 defeat of Angers prior to the international break.
Mbappe joined up with the France squad but, following medical tests, the French Football Federation (FFF) has confirmed it has allowed the player to leave Didier Deschamps' group.
Borussia Monchengladbach's Alassane Plea has been called up as Mbappe's replacement.
France face Iceland on Friday before meeting Turkey on Monday in Euro 2020 qualifying.
They are second in Group H on 15 points, the same as leaders Turkey.
Mbappe has only managed six appearances for PSG in all competitions this season, scoring twice.
The former Monaco star will attempt to regain fitness in time for PSG's next Ligue 1 match, which is against Nice on October 18.