PSG's latest blow adds to their injury problems with Neymar also set to miss their Champions League round of 16 match against Bayern Munich on March 8 after suffering ligament damage. Christophe Galtier's side trail 1-0 on aggregate ahead of their trip to the Allianz Arena.
Kimpembe, who missed the World Cup in Qatar due to a hamstring injury, was stretchered off early in the first half, two weeks after making his comeback from a three-month layoff.
In a medical update, PSG said: "Presnel Kimpembe has ruptured his right achilles tendon. He will undergo surgery to repair the tendon in the coming days."