The verdict was handed down by the LFP at a league disciplinary hearing on Thursday after Brandao left Motta with a broken nose after Bastia's Ligue 1 clash with PSG on August 16.
Brandao - in his debut season for Bastia - was provisionally suspended following the incident last month but has now been banned until February 22.
Bastia and PSG met at the Parc des Princes last month but the fixture was marred by an incident involving Brandao and Motta.
Video footage showed Brandao waiting for Motta in the tunnel following the full-time whistle, and the 34-year-old Brazilian was seen headbutting the PSG veteran before running away.
Brandao's actions were condemned by PSG president Nasser Al-Khelaifi, who called for the striker to be banned for life.
Despite the criticism and outcry, Bastia opted not to take action again Brandao, leaving it up to the French football authorities to hand down a punishment.
Brandao has only made two appearances for Bastia since arriving from French rivals Saint-Etienne at the start of the 2014-15 season.
