The man went missing from Kouaoua on the east coast and late yesterday a police search was still underway.
Reports say the man went to look for keys to a house during the cyclone and never returned.
Four people were slightly injured in the category three storm which is moving south away from the territory.
The president Philippe Germain said New Caledonia was left relatively unscathed by the cyclone.
He said Houailou on the east coast where Cook made landfall on the main island was among the most damaged areas.
About 5000 people in the suburbs of the capital Noumea were still without power yesterday due to fallen trees and wind gusts.
Photo: Supplied (The morning after the initial impact of Cyclone Cook in New Caledonia).