The sentence exceeded the prosecutor's request for an eight-month suspended sentence along with a 15,000-euro ($19,000) fine.
After Bastia's 2-0 loss to PSG in August, the Bastia striker waited in the dressing room corridor for 20 minutes after being substituted, and as the players came off he walked over to Motta and butted him in the face before running away.
Motta's nose was broken in the incident, and PSG president Nasser Al-Khelaifi called for Brandao to be banned for life.
Brandao's lawyer, Olivier Martin, told The Associated Press that the player will not be jailed, with his sentence likely to be served through community service.
"There has been too much media coverage and that resulted in a disproportionate decision," Martin said, adding that he has yet to decide whether to appeal the sanction.
The 34-year-old Brandao is currently hospitalized for surgery on a thigh injury and did not attend the hearing.
Brandao, a burly striker who had spells with Saint-Etienne and Marseille before joining the Corsican club, won the French league and two League Cups with Marseille from 2009-12. He has already been suspended for six months by French football authorities.