Emergency services were called to the A64 at Bilbrough top, near to the Aagrah restaurant at 7.58am on Monday following reports of a serious crash involving a silver Volkswagen.
The vehicle, which was travelling westbound, veered across the eastbound carriage and crashed into the central reservation, blocking the eastbound side.
The Yorkshire Air Ambulance also attended the scene and the road reopened at 9.30am.
Both the male and female in the car were taken by road ambulance to Leeds General Infirmary.
North Yorkshire Police has now confirmed both have been arrested.
"The female passenger was also arrested on suspicion of aggravated vehicle taking.
"Both are currently in police custody.
"A driver of another vehicle has also been spoken to as a voluntary attendee."