Neymar's suspension will begin on Monday, which means he will be eligible for Saturday's Ligue 1 match against Angers. He will miss PSG's final two league games against Dijon and Reims.
PSG said in a statement on Friday that they found the sanction 'severe' and that they were appealing it to the federation's appeal committee.
The 27-year-old will also miss the opening match of the new season, the annual Trophee des Champions match against Rennes in August. However, the suspended ban will allow him to play the next two games after.
Neymar has already been suspended for three Champions League games for insulting match officials following the French side's elimination in the quarter-final.
PSG were also fined 35,000 euros (30,204.8 pounds) after their fans used lasers and fireworks during the match.
(Reporting by Rohith Nair in Bengaluru; Editing by Amlan Chakraborty)
