The former Top Gear presenter was said to be filming a drag-style race when the accident occurred.
He was reportedly rushed to hospital after the incident but has since been given the all-clear, having been treated for a broken rib and given a brain scan.
According to the report in The Sun, the incident took place during a challenge in which May, alongside co-presenters Jeremy Clarkson and Richard Hammond, drove cars along a tunnel towards a rock wall at a Norwegian naval base.
It’s claimed that the accident was caused by a fault in the tunnel lights, which caused May to brake later than required while driving at 75 miles per hour.
Filming was reportedly abandoned but resumed again within a matter of days.
The Independent has contacted representatives for May and the show’s production company for comment.
The incident was not the first car accident to occur behind the scenes of The Grand Tour.
In 2017, Hammond was involved in a serious accident while travelling at a speed of 319 miles per hour.
After the front-right tyre failed, the car flipped over, damaging Hammond’s eye and requiring him to be cut out with hydraulic shears. He was taken to hospital, where he was in a coma for two weeks and later suffered from post-traumatic amnesia and a five-second memory.