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.
Officials were trying to trace Sage's movements since she returned to Papeete.
Travellers entering French Polynesia are expected to have a medical certificate showing they were free of the virus.
Mr Fritch has asked French Polynesians to put off all travel abroad.
The French president, Emmanuel Macron, has already postponed a long-scheduled visit to the territory next month.
To offset the arrival of the coronavirus, most Pacific countries have imposed strict border controls.
Countries including Vanuatu, New Caledonia, French Polynesia, and Tonga have brought in health checks and turned away cruise ships in recent weeks.