"Police will be making further inquiries into this crash to establish the cause," the spokeswoman said.
The vehicle smashed through a fence on the corner of Somme Pde and McNeil St, damaging several graves and breaking headstones.
On Monday morning a large amount of smashed glass and bits of a vehicle were strewn around a section of the old part of the cemetery.
A nearby resident said locals were fed up with the behaviour of drivers who regularly did burnouts and doughnuts on the roads outside and inside the cemetery and she was disgusted that graves and headstones had been damaged.
"Imagine how the families will feel," she said.
She suggested CCTV cameras be installed near the cemetery to deter hoons.
Another local, Fiona Donne, said people she had spoken to were horrified by the latest incident.
"I went to look at it and was talking to a man I knew who was there and two teenage girls came along - we all said how disrespectful to the whole area it is," Donne said.
"There are regular burnouts down the main road in the cemetery. This one looks like they came from Papaiti and missed the corner and went through the fence."
Cars regularly sped along Somme Pde but it was difficult to get registration numbers to report to police, Donne said.
"There are a lot of children up here, and children going to Churton School," Donne said.
"They have just last week put up one of those speed signs on one of the pillars but I doubt the people regularly speeding would even see it.
"You can't expect the police to sit up here all the time to try to catch them. They have enough to do."
Whanganui District Council parks officer Claire Lilley said the council was investigating whether the fence needed to be reinstated.
"We will follow up with the police with regard to any prosecutions and claims for damages," Lilley said.
The council would try to contact the families who owned the headstones and they could decide whether they wished to follow up on any prosecutions and claims for damages.
"We have been to look at the headstones and do not believe that they pose a danger to the public," Lilley said.
She was not aware of any regular incidents involving bad driver behaviour at the cemetery.