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.
"He will undergo surgery in the coming days," PSG said in a statement on Monday.
"His season is over," coach Fabien Galthie said.
Sunday's victory, in which Kylian Mbappe and Lionel Messi scored, extended PSG's lead to eight points. They host Nantes on Saturday.