President Edouard Fritch said the carrier was one of French Polynesia's members of the French National Assembly, Maina Sage, who returned from Paris at the weekend.
Ms Sage was at home in self-isolation, Mr Fritch said.
Reports say she had met the French culture minister Franck Riester, who has also been infected.
Mr Fritch said before returning to Tahiti she had a medical check-up that showed no sign of the illness.
Amid concern over the spread of the virus, she then reportedly arranged for a test which came back positive.