Around 500 people gathered in the French Mediterranean island's capital Bastia a day after the clashes in Sisco, on the north of the island.
The dispute erupted between members of "three families of North African origin and young locals", prosecutors said in a statement, adding that stones and bottles were thrown and three cars went up in flames before police managed to restore calm.
A girl who witnessed Saturday's clashes, speaking to Sunday's rally through a megaphone, said they began after tourists took photos of several women bathing in burqinis. According to the girl, whose account however could not be verified, a group of immigrant origin youths shouted insults, before several older men arrived, carrying hatchets, in support of the families on the beach.
They attacked a group of young Corsicans aged 15 to 18 on the beach, whose role in the incidents was not immediately clear. The girl said the young Corsicans' families then took to the streets and clashed with the North Africans. Two of the locals were injured by a harpoon, she said.
North African women slashed several car tyres, while locals set fire to two cars and overturned another that belonged to immigrant families. The clashes injured five people, all of whom were discharged from hospital by late Sunday, prosecutors said, adding that no arrests were made.
On Sunday demonstrators held talks at the local government office late in the morning. Afterwards, in tense scenes, the crowd called to be allowed to head up to the Lupino district of Bastia, which has a large North African community.
"We're going up there because this is our home," they said. Police blocked them from entering the area. Up to 100 members of the security forces were deployed to restore calm, police said.
French Interior Minister Bernard Cazeneuve condemned the violence, and pledged a full investigation "to shed light on these intolerable deeds and to arrest those responsible".
The clashes come amid heightened tension in France after a string of attacks claimed by the Islamic State group, including the July 14th massacre in the southern city of Nice when a Tunisian ploughed a truck into crowds celebrating Bastille Day, killing 85 people.
In Corsica last December, angry protesters vandalized a Muslim prayer hall and trashed copies of the Koran after an assault on firefighters that was blamed on local youths of Arab origin. The nearby French Riviera resort of Cannes has also sparked controversy by declaring a ban on burqinis - a ruling which won a court backing at the weekend.
Islamic dress has long been a hot-button issue in secular France, where the full-face veil is banned in public places.
Last month Corsican lawmakers called on the French state to close down radical mosques on the island, hours after an underground separatist movement issued a threat against Islamic extremists.
A splinter group of the nationalist Corsican National Liberation Front (FLNC) warned Islamists that any attack on the island would trigger "a determined response, without any qualms".