Coast guard officers were able to rescue 15 passengers on the boat after it foundered on a coral reef.
A rescue team rushed to the scene after the boat was picked up on radar in the early morning. They finally found the vessel after hearing cries for help, the prefect's office said in a statement.
The survivors were taken to hospital while a helicopter searched for one person still missing.
Such accidents are common in Mayotte, part of the Indian Ocean archipelago of the Comoros that opted to remain under French rule when three other islands chose independence from France in 1975.
Many people from the nearby Cormoro islands, hoping to find work or medical care in Mayotte, board rickety fishing boats to attempt the risky journey, often running aground on coral reefs.
Some two-fifths of Mayotte's 200,000 inhabitants are thought to be illegal immigrants.