The men, aged between 24 and 30, have no criminal record and are believed to belong to an Islamophobic movement but not to any political party, public prosecutor Eric Bouillard said.
The prayer hall on a housing estate in the Corsican capital Ajaccio was trashed, along with a nearby kebab shop, and several copies of the Koran damaged when a group, shouting "Arabs out!" or "This is our home!" in the Corsican language, attacked them on 26 December.
Bouillard said that searches of premises, which should provide more evidence of involvement in the attack, would be organised.
The incident occurred on the sidelines of a demonstration in support for firefighters and police officers who had been attacked on the estate the previous day.
Criticism of investigation
The fact that 11 people had been charged with involvement in that attack but nobody for the assault on the prayer hall had led to accusations of a lack of enthusiasm in the latter inquiry.
Joseph Maestracci of the Ava Basta (That's enough!) anti-racist group told the Mediapart website earlier this month that they had been caught on CCTV and mobile phone videos and "recognised by everybody", while Muslim leaders pointed out that estate residents and the prayer hall's administrator had lodged civil cases.
In February a machine gun was fired at a halal butcher's and a kebab restaurant in Propriano, south of Ajaccio, and there was a suspected arson attack on another Ajaccio prayer hall on 30 April.