Francois-Xavier Bieuville, the island's prefect, told local media the death toll could rise significantly once the damage is fully assessed. He warned it will "definitely be several hundred" and could reach the thousands.
French Interior Minister Bruno Retailleau, who is scheduled to visit the island to assess the damage and coordinate further relief efforts, acknowledged the "exceptional severity" of the cyclone and assured that efforts to assist the population are being ramped up.
Cyclone Chido also made landfall in Mozambique, where it brought flash flooding, uprooted trees and damaged buildings about 25 miles (40km) south of the northern city of Pemba.
The cyclone caused structural damage and power outages in the northern coastal provinces of Nampula and Cabo Delgado on Saturday morning, authorities reported.
Guy Taylor, a spokesperson for aid agency Unicef in Mozambique, said "we were hit very hard in the early hours of this morning".
"Many houses were destroyed or seriously damaged, and healthcare facilities and schools are out of action," he added.
Mr Taylor said Unicef is concerned about "loss of access to critical services", including medical treatment, clean water and sanitation, and also "the spread of diseases like cholera and malaria".