The head-butt landed on Paris Saint-Germain midfielder Thiago Motta by Bastia striker Brandao has been described as "scandalous" by French secretary of state for sports Thierry Braillard.
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The incident came in the tunnel at full-time after PSG's 2-0 win against Bastia, leaving Motta with a broken nose.
"Of course it merits a sanction," Braillard told France Info, calling Brandao's action "scandalous, unacceptable".
This is not the first time the Brazilian has come under scrutiny for poor conduct on the pitch.
Brandao was suspended for four matches after elbowing Yohan Cabaye in a match between St Etienne and PSG at the Parc des Princes last season.
In the immediate aftermath of the incident, PSG president Nasser Al Khelaifi called for Brandao to be suspended for life. However, 24 hours later, L'Equipe.fr reported that neither the club nor Motta wanted to aggravate the situation by bringing formal charges
Despite that, French police are reportedly ready to open their own investigation into the matter while the French Football League's Disciplinary Commission will also launch a probe.
The LFP is set to examine the incident on Thursday and depending on the gravity of Motta's injury and his subsequent absence, Brandao could face up to a 12-month ban from French football authorities.
Though RMC reported on Sunday that Bastia may sack the former Shakhtar Donetsk forward, who only joined the club on a one-year deal earlier this summer, the Ligue 1 outfit issued a statement insisting no sanctions would be taken against Brandao until Monday.
The striker, who took on French citizenship earlier this year, spent the previous two French top-flight seasons at St Etienne. His assault on Motta took his former boss, Christophe Galtier, aback, and the coach claimed it was entirely out of character.
He said: "Brandao is a player who, given his athletic build and style of play, comes into contact with other players, sometimes it's unlucky, sometimes it's borderline, which lead to suspensions or tempers fraying.
"I have never seen him get annoyed in the dressing-room nor in the tunnel. I'm surprised. I don't know what happened on the pitch, if there were things said or not, but the act he committed can hardly be forgiven."