The incident happened on Thursday night near the Sunhaven Beach Bungalows.
The motor vehicle is believed to be travelling towards town when it veered off the road and crashed into the graveyard.
Police Inspector Solomona Tuaati said police were “looking into” the incident.
He said the driver of the vehicle was missing from the scene when police attended the crash on Thursday night.
“We are investigating the matter and there is nothing else I can say at this moment,” Tuaati said.
Careless and drink driving cases have been on the rise in Rarotonga and police is calling on the public to report any incidents of dangerous or reckless driving to them.
Police spokesperson Trevor Pitt said many calls about such driving behaviour were fielded and registrations of the vehicles were always followed up and pursued.
In many cases, the offenders are charged or warned, he said.
“It's true that driving behaviour has not improved on Rarotonga. At times it's disgraceful. The driving culture is substandard given the need to adapt to road conditions (surface and width) and increased number of vehicles,” Pitt said.
“Unless those factors are adequately addressed it is only the police who are burdened with the responsibility of road safety.”
Pitt said the police have tried to put in measures to help improve the poor driving culture on the island. He said testing and the fees to cover it and the helmet law were part of it.
But without any assistance with resources or improved levels of personal responsibility, he said it would just be down to enforcement of the law.
Pitt also said there was room for a new look at penalties, including monetary fines and loss of vehicles, and driving privileges to curb dangerous driving in Rarotonga.
“The expectations are that the police are supposed to make sure drivers are licensed. Police have to stop the speedsters, police have to catch the reckless drivers, police have to prevent the drunks from driving etc, etc.
“(But) when do people actually take responsibility themselves? Everybody's seen reckless behaviour, risky overtaking, driving with people sitting up on the sides of truck trays and carrying kids in front on bikes.”
Pitt said traffic infringements were clogging up the system at the High Court.
“It’s also appalling to see a number of drivers trying to get off alcohol charges and refusing to be tested. No responsibility - leave it up to the police.”