PSG won the match at the Parc des Princes 4-0 to claim their second victory of the season.
Mbappé, 20, limped off in the 66th minute while Cavani did not even last the first 15 minutes. The 32-year-old Uruguayan came off clutching his hip and was replaced by Eric Choupo-Moting.
The Cameroon skipper made the most of his opportunity. He broke the deadlock in the 50th minute and a Martin Goncalves own-goal five minutes later doubled PSG's advantage.
Choupo-Moting secured the points with his second goal after 75 minutes and Marquinhos added the gloss seven minutes from time.
Mbappé's injury to his left hamstring means he will miss PSG's opening Champions League group game, which is set for 17 or 18 September.
He is also set to sit out three league matches as well as France's Euro 2020 qualifiers at home to Albania and Andorra next month. Cavani could though return in time for the Champions League match.
The injuries hit PSG coach Thomas Tuchel as doubt continues to cloud the future of 222 million euro striker Neymar.
The Brazilian's desired move back to Spain has not materialised with a week remaining before the European transfer window closes.
However even if he were to stay at the French champions, he will be of no use for the initial assault on the Champions League.
The 27-year has to serve a three match ban following comments about the officiating during PSG's last 16 loss to Manchester United at the Parc des Princes in March.