The Georgian winger suffered a suspected anterior cruciate ligament injury in the 4-2 Champions League win over Barcelona.
Kvaratskhelia was forced off the pitch in the 59th minute and replaced by Maghnes Akliouche.
He could potentially be sidelined for up to nine months, but will wait for a MRI scan on Wednesday to determine the extent of the injury.
Kvaratskhelia's injury wasn't the only blow for the French champions as Marquinhos and Ousmane Dembele were also both substituted in the match, with the former replaced with Illia Zabarnyi on the hour mark with a suspected hamstring strain, as Dembele limped off the field in just the 20th minute.
Speaking after the game, PSG boss Luis Enrique told reporters: "I am not the doctor. I am the coach.
"The three injuries is the worst part of the game today.
"We will have to wait for the tests tomorrow. They are three very important players, so it's really bad news, of course, but that's football."
Paris St-Germain produced a thrilling performance to defeat Barcelona in the Champions League, ending the Spanish side's 11-match unbeaten start to the season with a 4-2 victory at the Parc des Princes.
Barcelona midfielder Pedri has jokingly warned his close friend Ferran Torres not to score when the Catalan side face Paris Saint-Germain in a major Champions League clash tonight at Parc des Princes.
Barcelona coach Hansi Flick is considering using Frenkie de Jong in defence for Tuesday's Champions League clash against Paris Saint-Germain as injuries leave him short of options at the back.
Paris Saint-Germain manager Luis Enrique has admitted his side were fortunate to beat Manchester City 4-2 after surviving a fierce second-half comeback to maintain their perfect start to the Champions League.
