The Brazil star was stretchered from the pitch in tears after suffering the injury in the final minutes of Sunday's 3-1 victory at Saint-Étienne.
"The examinations carried out last night confirm that Neymar Jr. is suffering from a sprained left ankle with ligament damage", PSG said in a statement, adding that a further update would be made in 72 hours.
Neymar had started 13 of the past 15 games for PSG this season after an injury-plagued four years in France, but he faces another lengthy absence after landing awkwardly following a challenge by Saint-Etienne's Yvann Macon.
The 29-year-old posted a video of himself wearing a pressotherapy boot on his left leg. "These runs of bad luck are part of an athlete's life", he said Sunday on Instagram. "That's the way it is now, you have to pick yourself back up and move forward. I'll be back better and stronger".