The United States Embassy, the British High Commission, the French Embassy and the New Zealand High Commission were among damaged buildings housed in the same complex.
US officials said the building sustained "considerable damage" and would be closed until further notice. All staff in the building had safely evacuated, they added.
Separately, several Australian airlines have also cancelled flights into Port Vila, citing damage at the airport.
Australian carrier Jetstar, subsidiary of Qantas, cancelled a flight scheduled for Wednesday morning from Sydney to Port Vila, citing "earthquake activity in Vanuatu and reports of possible damage to Port Vila airport infrastructure".