Both players suffered the injuries in the reigning European champions' 4-2 league phase win against Barcelona at the Parc des Princes on Tuesday.
"Having suffered a torn anterior cruciate ligament in his right knee during yesterday's match against FC Barcelona, Khvicha Kvaratskhelia is set to undergo surgery in the coming days," PSG said in a statement, without giving a timeline for his recovery.
Recovery from ACL surgery typically takes between six and nine months, meaning the 25-year-old Georgia international can at best hope to return for the closing stages of the season.
Former Napoli winger Kvaratskhelia has established himself as one of Europe's most exciting attacking players and played a leading role in helping PSG to win back-to-back Champions League titles in the last two seasons.
PSG boss Enrique plays down perfect start to defence of Champions League crown
Like Dembélé, he is one of the contenders for the Ballon d'Or, which will be awarded on Monday.
The club said Dembélé, the current Ballon d'Or holder, and influential Brazilian central defender Marquinhos will both be sidelined for "several weeks" with thigh injuries they suffered in the win against Barcelona.
Kvaratskhelia slumped to the turf without any apparent contact and left the pitch just before the hour mark on Tuesday.
Dembélé, 29, had to be substituted after 20 minutes due to his injury.
In the absence of two of their attacking stars, PSG will need to rely on summer signings Maghnes Akliouche, Mika Godts and Ferran Torres, the Spain international who scored the winning goal in the World Cup final in July.
PSG are away to Ligue 1 leaders Lyon on Sunday in their next domestic match and they travel to Spanish side Villarreal for their next Champions League fixture on November 3.



YEA deploys over 11,700 youth under Community Police Assistant Model – Basintale
Parliament’s Human Rights Committee demands swift investigations in Obuasi SHTS ...
'Let the law take its course' – Veep on Obuasi SHTS sexual abuse allegations
Obuasi SHTS sex scandal: 'The powerful ride the law to trample the weak' – Kofi ...
19-year-old remanded over alleged fatal stabbing of boyfriend at Ofankor
Woes of SHTS Headmaster deepen as he resigns as old students’ chairman
'NPP has 35 NDC scandals to drop from now till 2028 elections' — Sammi Awuku
'NDC will pay for Obuasi SHTS sex scandal' – Sammi Awuku warns
Use of hormonal contraceptives linked to increased breast cancer risks – Doctor ...
ECOWAS deepens EU cooperation to improve disaster response in West Africa
