The male rider, who has not been named, came off his bike at the privately-run event next to Low Hardwick Farm, near Sedgefield, at about 13:00 BST.
He was taken by air ambulance to hospital in Middlesbrough but was confirmed dead shortly before arrival.
The woman, in her early 30s, suffered serious injuries at about 14:10 at which point the event was closed.
The female rider was also taken to the James Cook University Hospital by air ambulance, police said.
A spokesman for Durham Police said: "We took the decision on safety grounds to close down the privately-run event, which involved around 100 participants and 300 spectators.
"We understand the formal investigation is likely to be led by the local authority, but we are carrying out initial inquiries into the circumstances.
"With two very serious incidents within little more than an hour, we felt there was little choice but to bring the event to a close."
The site is regularly used for motocross and quad bike events.
The organisers have not been available for comment.
A man has died and a woman has been seriously injured at a quad and motocross event in County Durham.