According to weather forecaster Météo-France, the storm passed approximately 100 km (62 miles) south of Mayotte around 09:00 GMT.
“Extremely heavy rains are starting to fall,” Francois-Xavier Beauville, prefect of Mayotte, told French news channel BFMTV.
They caused the first floods “and relatively significant landslides” across the territory, he added.
The prefect said the island was likely to remain on red alert until Monday evening as heavy rain was expected to continue even after the storm passed.
At least 14,500 people took shelter in emergency shelters set up to protect against the storm, BFMTV reported.
As of Sunday afternoon, the storm was moving away from Mayotte, according to Météo-France. The system is expected to slowly intensify over the next 24 hours to tropical cyclone status as it approaches the coast of Mozambique.
The current forecast does not call for landfall in Mozambique, but “very deteriorated conditions” are still expected in the Nampula region, the forecaster said.
Mozambique is also recovering from Cyclone Chida, which killed 120 people in the country.