The two players were involved in an on-field spat over set-piece duties.
Cavani and Neymar argued over a penalty during the second half. The Uruguayan, who is PSG’s usual penalty taker, won the tussle but saw his spot-kick saved.
According to L’Equipe, tensions rose further in the dressing room afterwards.
Cavani left the pitch immediately after the full-time whistle, not joining the rest of his team-mates in waving to the club’s supporters.
He waited in the dressing room for his teammates to arrive and then reportedly stopped Neymar in his tracks, telling him in Spanish that he was unhappy with the club’s new poster boy’s attitude.
According to witnesses, Neymar responded before Cavani stood up and went face-to-face with the Brazilian, only for club captain Thiago Silva and Marquinhos to intervene.
Cavani is said to have showered and left through a back door, avoiding the mixed zone at the Parc des Princes, within 20 minutes of the final whistle.