Tairāwhiti area commander Sam Aberahama said the sole occupant of the vehicle had minor injuries and was taken to hospital.
"We appreciate that hearing this news will cause distress for those who have whānau buried at this cemetery and we have been in contact with the Gisborne District Council tonight in relation to this damage."
A kaumātua would also be at the cemetery on Wednesday morning to bless the site.
The area would remain cordoned off and under guard overnight, Aberahama said.