"Based on all available data ... the tsunami threat from this earthquake has now passed," the agency said on its website.
The evaluation was repeated on Twitter by France's High Commission in the French territory in the South Pacific, which thanked those who had shared information online about the quake.
"All tsunami warnings raised in Caledonia - thank you for your shares," the high commission wrote.
The epicentre was located 82km northeast of the town of Tadine in the country's Loyalty Islands, which lies in the South Pacific's Ring of Fire.
The quake, at a shallow depth of 10km below the seabed, triggered tsunami waves, the Hawaiian agency said. It warned of "hazardous tsunami waves" for coasts within 300km of the epicentre.
The quake was followed minutes later by a magnitude-5.1 tremor about 14km closer to shore and at the same depth.
Public broadcaster Nouvelle Caledonie 1ere posted photos on its Facebook page of the damage caused by tremors on Mare, the second largest of the Loyalty Islands.
Large cracks appeared across roads and residents were forced to clean up smashed bottles and damaged products which had fallen from supermarket shelves.
Other pictures on Nouvelle Caledonie 1ere's website show abandoned vehicles as people evacuated the town of Medu on Mare's south-western coast.
New Caledonia, popular with tourists for its beaches and coral reefs, is located around 1,500km east of Australia.
