The forward was hurt by a strong challenge from Loic Perrin, who was sent off, in PSG's 1-0 victory over Saint-Etienne in Friday's Coupe de France final.
The France star was seen on crutches while celebrating the win with his team-mates and underwent tests on Saturday.
PSG announced in a statement that he has a "serious right ankle sprain to the external lateral compartment. To be re-evaluated in 72 hours with clinical and ankle imaging analysis".
Mbappe is likely to be a doubt for PSG's Champions League quarter-final clash with Atalanta, which takes place in Lisbon on August 12.
He is also expected to miss the rearranged Coupe de la Ligue final against Lyon on July 31.
Earlier on Saturday, Mbappe posted on Twitter: "Waking up as a winner, there's no better feeling possible. Thank you all for your messages, I'm deeply touched. Kisses to all and have a good weekend."
⏳👊🏽🙏🏽.— Kylian Mbappé (@KMbappe) July 25, 2020
Réveil en tant que vainqueur, pas de meilleure sensation possible.
Merci à tous pour vos messages, ça me touche beaucoup.
Bisous à tous et bon week-end 😀 pic.twitter.com/gwTI48KXrm
PSG also confirmed Thilo Kehrer will be out of action for four to five days after sustaining bruising to his right hip bone.
However, Abdou Diallo and Juan Bernat are set to resume full training on Monday.