Four people are in custody with further arrests expected after Nice fans invaded the pitch following Saturday's 1-0 home loss to Bastia.
Around 100 fans, members of the Populaire Sud ultras group, charged onto the pitch at the Allianz Riviera, sending both sets of players running for safety.
The incident was sparked when Bastia's substitute goalkeeper Jean-Louis Leca brandished a Corsica flag during the postmatch celebrations, provoking an angry reaction from Nice captain Didier Digard.
"There were words exchanged between Bastia and Nice players, but nothing more," Bastia defender Francois Modesto was reported as saying by L'Equipe.
"Then suddenly we saw fans and stewards charging towards us. We were hit from behind."
The four people who have been remanded in custody are likely to be joined by more, with police examining video surveillance footage.
"I wasn't afraid, but I was annoyed with the Bastia player," Digard told L'Equipe. "All our supporters did was push the Bastia players to the dressing room, to show them that they were in their place."
Leca told Canal+ on Sunday he "had no reason to apologise" for his actions, despite them being in contravention of a local authority ban on any Corsican symbols of Corsica being present inside the stadium -- a ban imposed because of the long-running animosity between the two clubs.
Bastia issued a statement on their official website which said they would not "accept any punishment of Jean-Louis Leca" and blamed Digard.
"Contrary to what has been claimed, Jean-Louis Leca absolutely did not go towards the Populaire Sud to provoke them, but rather to go to the centre circle to join the rest of the team," the statement read.
"The incidents were sparked only because the Nice captain Digard thought it was a good idea to go and aggressively tell our player that he should put away his flag and his identity."
Nice are likely to face either having to play a game behind closed doors or at a neutral stadium after the French Football League (LFP) president Frederic Thiriez promised that action would be taken.
"The things that happened at the end of the Nice and Bastia game are worrying and unacceptable," he said in a statement.
"Such images of a pitch invasion and fights between players and supporters, even if, incredibly, no serious injuries occurred, should no longer be seen in football."
The LFP's disciplinary commission will review the matter on Thursday, and Thiriez encouraged it to "attribute responsibility so that the inevitable sanctions can be taken."