Brandao appeared to headbutt the Italian midfielder in the tunnel following his side's 2-0 defeat to the French champions on Saturday,
PSG later confirmed that Motta had sustained a broken nose, while Bastia "unequivocally condemned" their player's actions.
Bastia opted to leave any punishment up to the French football authorities, with PSG president Nasser Al-Khelaifi calling for Brandao to be banned for life.
On Thursday it was confirmed the LFP had suspended Brandao until a hearing on September 18.
The 34-year-old is in his first season at Bastia after joining from Saint-Etienne, but will now miss at least three Ligue 1 fixtures - against Toulouse, Bordeaux and Lens - before his hearing next month.
Get the best features, fun and footballing frolics straight to your inbox every week.
Thank you for signing up to Four Four Two. You will receive a verification email shortly.
There was a problem. Please refresh the page and try again.