The tremor at 2254 UTC was recorded at a depth of 10 kilometres.
The Pacific Tsunami Warning Center in Hawaii says waves of between one and three metres could hit French Polynesia.
Waves of up to a metre are forecast for New Caledonia, New Zealand, Fiji, the Samoas, the Cook Islands, Tokelau, Vanuatu, Kiribati, Tonga, Solomon Islands, and the scattered islands over the north Pacific.
Smaller waves may hit Tuvalu, Papua New Guinea and Nauru.