Neymar has been banned for three games by the French Football Federation following an investigation into his altercation with a spectator after Paris Saint-Germain's Coupe de France final defeat to Rennes.
Neymar, who appeared to hit a member of the crowd while on his way to collect his runner-up medal after the defeat on penalties, could have faced a ban of up to eight matches for the incident.
The punishment, which includes a suspended ban for a further two matches, means the Brazil international will miss PSG's final home game of the season against Dijon, the campaign-ending trip to Reims and the Trophee des Champions against Rennes in August.
PSG said they would appeal against the punishment, which they described as "severe."
"Considering the insults suffered by several of the club's players, including Neymar, at the end of the Coupe de France final, plus the various elements sent by PSG to the disciplinary commission, we consider this sanction severe," a club statement said.
"PSG and Neymar have decided to appeal against this decision to the FFF's commission for higher appeals."
Speaking at a news conference ahead of Saturday's trip to Angers, coach Thomas Tuchel said: "The penalty is normal. Neymar made a mistake, so he must accept it. We must accept it."
Meanwhile, sources have told ESPN FC that an appeal against Neymar's three-game Champions League ban is ongoing.
He was banned for three European games for insulting match officials on social media after PSG were eliminated from the tournament by Manchester United and will miss half the group stage next season.
Neymar has scored 22 goals and contributed six assists in 26 appearances in all competitions this season.
Despite a second consecutive lengthy injury layoff, he is in contention to win the Ligue 1 Player of the Year award.
Asked whether the Brazil star could become PSG captain in the future, Tuchel said: "There are many ways to show leadership.
"Neymar is an artist, creative, and can lead through his quality. He is not the same sort of leader as Marquinhos, Thiago Silva or Gianluigi Buffon. I am happy with Marquinhos and Thiago, so I will not be changing that."