Singly was taken to the only hospital in Réunion equipped to deal with diseases like Ebola but officials insisted that she was not contagious.
“A person only becomes contagious when they have experienced a high temperature, vomiting, a soar throat and haemorrhaging,” local official Dominique Sorin told a press conference.
Singly had recently returned to Réunion after carrying out humanitarian work in Ebola-hit Guinea in west Africa, Sorin said.
Blood samples are currently being analysed in a laboratory in the French city of Lyon to establish whether she had Ebola.
This is the first suspected case of Ebola in Réunion.
A suspected case on the neighbouring island of Mauritius in September turned out to be malaria.
The French health authority which covers the Indian Ocean islands has put in place measures for the prevention of transmission.
There is a “very slight” risk that the virus could be imported from the European Union, they say.
Over 6,500 people have died of Ebola in west Africa, according to the World Health Organisation.