Richard Hammond, a 36-year-old television presenter, was filming for the programme at a disused airfield in York, central England, when the accident happened late Wednesday afternoon local time.
He was involved in a high-speed car crash while filming an apparent attempt to break Britain's land speed record.
Hammond was behind the wheel of a jet-powered car that travelled at speeds close to 482.8 kilometres per hour.
The current British land speed record is 483.286 kilometres per hour, held by Colin Fallows, who set the record in 2000.
A former firefighter at the scene said the accident had happened on the last attempt of the day, which saw the car veer to the right, triggering the deployment of one of the parachutes.
The car, however, went onto the grass, and "spun over and over" before eventually resting upside down and "dug in" to the grass, Dave Ogden of Event Fire Services said.
Hammond was cut free, placed in a neck brace and onto a stretcher before an air ambulance arrived to take him to hospital.
A BBC spokeswoman provided few details saying only: "The incident happened quite recently and the focus of our attention is on Richard at this stage".