"The sanction appears to be disproportionate," Olivier Martin told sports daily L'Equipe's website.
"The player, whose career can be threatened by this decision, has decided to appeal."
It was the second time in two seasons the former Olympique de Marseille player has been suspended for foul play. Brandao also received a three-match ban last season for elbowing another PSG player, Yohan Cabaye.
Security camera footage broadcast on French television after this season's game, and replayed repeatedly, showed Brandao standing near the middle of the corridor outside the changing rooms at the Parc des Princes after the Corsicans' 2-0 defeat by the Ligue 1 champions.
Facing the camera as Thiago Motta strides into view, Brandao, who was replaced during the game after picking up a yellow card, calmly takes two steps forward before leaning in to make contact with the Italy international's face.
He then turns and runs away with Thiago Motta in pursuit.
Separate footage on Canal+ television showed blood pouring from Thiago Motta's nose. A medical report from PSG said the midfielder's nose was broken.
Bastia said at the time of the 34-year-old's head-butt that they "condemn without ambiguity" the player's actions but also "deplore the behaviour of certain players who never stop insulting and provoking their opponents".
Nasser al-Khelaifi, PSG president, said that Brandao should be banned for life.
French league rules allowed for a maximum ban of two years.
(Reporting by Julien Pretot; Editing by Ed Osmond)
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