The vehicle was allegedly set on fire during the early hours of Sunday, 1 January.
Neiafu Town officer Vava Lapota said the incident happened at around 3am while the car was left unattended on a road from Holonga to Ta’anea.
Kaniva News reports the car belongs to a Pentecost Church pastor.
It broke down before the pastor and his family sought help from a nearby village, Lapota said.
When they arrived back at the scene with a helper the car had been torched and destroyed.
Photos of the burnt-out vehicle showed the car was extensively damaged and it appeared that the windows had been smashed.
It is understood Police are seeking a person of interest.
Photo supplied