The diagnosis comes two and a half weeks before PSG are due to face Atalanta in Lisbon on August 12.
Mbappe was hurt in the second half of PSG's 1-0 win over St Etienne in the Coupe de France final on Friday night.
A PSG statement on Monday said: "The imaging workup performed today confirms a sprained ankle with external ligament injury. Following this trauma, the recovery time is estimated at around 3 weeks."
The 21-year-old, who has scored 30 goals in 34 appearances this season, has already been ruled out of Friday's Coupe de la Ligue final against Lyon but will hope he can beat the recovery timetable to have some involvement against Atalanta.
Additional reporting by PA.