The Brazilian was handed a provisional four-week ban the week after the incident but the full case has now been assessed.
"Brandao will be available to play again on Feb. 22, 2015," the league's disciplinary committee said in a statement.
It is the second time in two seasons the former Olympique Marseille player has been suspended for foul play. He 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 in the days afterwards, showed Brandao standing near the middle of the corridor outside the changing rooms at the Parc des Princes in Paris after the Corsicans' 2-0 defeat at the hands of 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 headbutt it "condemns without ambiguity" the player's actions but also "deplores the behaviour of certain players who never stop insulting and provoking their opponents".
Nasser al-Khelaifi, PSG president, said immediately after the incident that Brandao should be banned for life.
French league rules allowed for a maximum ban of two years.
(Writing by Mark Meadows; Editing by Greg Stutchbury)
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