The fire broke out about 1am Monday local time.
Police are investigating the cause of the fire in Port Vila.
The Malvatumauri Nakamal is a custom parliament for all Vanuatu's chiefs.
"This Nakamal was the identity of the people of Vanuatu. It symbolised the unity of the custom of the Vanuatu and the law, peace and order of communities in Vanuatu," said Chief Willie Plasua.
He told all chiefs around the country that while it is a major loss, it is only temporary.
"Custom, culture and tradition will never die and we will rebuild our headquarters," Plasua said.
RNZ Pacific correspondent Hilaire Bule said the cost of the Nakamal was more than 100 million Vatu - about $US850,000 - and was co-financed by the Vanuatu and Australian governments.
The house was built with local materials to house the members of Malvatumauri during their annual general meeting.
An eye-witness, Sylverio Molkis, said on seeing the fire he made several phone calls to the fire brigade but could not get through.
"I also called the police but there was no answer and I hade to go myself to the fire station to tell them about the blaze," he said.
Only two buildings housing the administration offices of the Malvatumauri have survived.