One woman was injured on Wednesday's incident, which led to dozens of nudist sunbathers fleeing Carataggio beach near Porto-Vecchio.
Witnesses said the man had threatened the group if they did not get dressed.
When they refused, he allegedly pulled out a rifle and started firing.
The injured woman, reportedly in her thirties, was hit in the thigh as she ran away.
The suspect - whose identity has not been revealed - owns a beachside cafe, police said on Friday. One man had been questioned in connection with the shooting but had since been released.
Despite being famous among nudists, the beach is not an official naturist site and locals have complained about their presence there.
A shootout on a beach popular among naturists on the French island of Corsica was caused by a local businessman who disagreed with their presence there, police say.