The incident happened yesterday as parents were dropping off their children at the start of the school day in Bonifacio, on the island's southern tip.
The two women, wearing Muslim headscarves, "were stopped by two men, two brothers, who thought it wasn't right that their children are not allowed to wear emblems of their religion at school and yet these women could enter with their veils," said local prosecutor Eric Bouillard, confirming a report in the Corse-Matin newspaper.
Bonifacio mayor Jean-Charles Orsucci said his education official "had intervened to allow normal entry to the school". Police and a schools inspector were also sent to the scene "and the situation calmed down.
There was no violence, no threats, and therefore no laws broken," said Bouillard. While religious symbols are banned for pupils and teachers in French schools, there is no such constraint on parents.
The incident is the latest example of intercommunal tensions in France. A burkini ban by local authorities in a string of resorts in southern France divided opinion and ended up in the courts.
A Nice court finally suspended its ban on the Islamic swimsuit on Thursday after authorities there had defied a ruling by the country's highest administrative court.
The string of bans came after the full-body swimsuit allegedly sparked violent clashes in Corsica -- in the latest in a series of incidents that have raised tensions between local Muslims and their neighbours.
In December, protesters vandalised a Muslim prayer hall and trashed copies of the Koran after an assault on firefighters that was blamed on youths of Arab origin.