Emergency services were called to the accident on private land at Fingle Woods on the edge of Dartmoor, Devon at about 14:25 GMT on Saturday.
The passenger was injured and taken to the Royal Devon & Exeter Hospital.
Organisers said the accident happened when an open car failed to climb a steep hill and backed down before rolling.
The driver of the vehicle is yet to be formally identified.
The incident occurred during the 88th Exeter Trial, organised by The Motor Cycling Club (MCC).
More than 300 cars and motorbikes were taking part in the event across large parts of the South West.
As part of the event, there are several sections on private land where the vehicles use rough tracks.
Roger Ugalde, clerk of the course for the MCC, said: "We don't know why it happened. The car has been taken away by the police for forensics to be carried out."
"It's thought something like this might have happened in the 1950's but since then there has never been a fatality at an MCC event," he added.
The Motor Sports Association (MSA) said: "A trial is a low-speed type of motorsport in which competitors aim to drive as far as possible up a hillside course.
"The MSA sends its sincere condolences to the family and friends of the deceased and offers the injured competitor its very best wishes for a full recovery".
A man has died after the car he was driving rolled while trying to climb a steep hill at an organised motor event.