Jules Gedeon, the Seychelles director for community health, said the number of people diagnosed with "chikungunya" was steadily rising since it was first reported in November and nearly 1,000 cases had been reported in January alone.
"We are still counting, but the number is quickly approaching 1,000 for this week," Gedeon told AFP, adding the country's security forces had been drafted for a nationwide mosquito eradication drive to stall the spread.
In addition, the health ministry announced Thursday it would take legal action against people who do not take measures to control mosquito breeding on their property.
Authorities in Madagascar and the overseas French territory of Reunion, where some 45,000 new cases have been reported since mid-December, have reported outbreaks.
Last week, the French government drafted 400 extra troops to help fight the mosquitoes that have been spreading the disease across Reunion since March.
On Madagascar, about 800 kilometers (500 miles) west of Reunion, a health official said Thursday that two more people had shown symptoms of the disease after dozens flocked to a hospital on the eastern side of the island with similar complaints in the past two weeks.
"Two patients admitted today at Toamasina hospital they had joint pains that strongly point at chikungunya," Mosa Milasoa, an official in Madagascar's health ministry, told AFP.
"Chikungunya" is Swahili for "that which bends up" and refers to the stooped posture of those afflicted by the crippling and extremely painful disease for which there is no known vaccine or cure.
It is characterized by high fever and severe rashes, and while non-fatal in itself and most people eventually recover, it can provide opportunities for other diseases to set in.
Health officials in the Seychelles attributed the recent sharp rise in cases of chikungunya to heavy rains that have been pounding the island since December.
No deaths have so far been reported, but it has affected several businesses as infected people have stayed home from work and the transport sector has been badly hit with bus schedules interrupted as drivers fall sick, they said.