The tractor overturned in the collision, on the A170 near Thornton-le-Dale at about 10.45am yesterday.
Police said the green Mitsubishi Shogun had been travelling in the direction of Scarborough after being requested to stop by police and failing to do so.
A passenger in the Mitsubishi received serious injuries and was taken to Scarborough Hospital for treatment.
The tractor driver and another passenger in the Mitsubishi were left with minor injuries.
The road was closed until 5pm to allow police to carry out a full investigation of the scene and for the road surface to be cleared.
A 29-year-old man from Redcar has been arrested on suspicion of dangerous driving and failing to stop. He currently remains in police custody.
Police are keen to trace anyone who was travelling along the A170 between Thornton-le-Dale and Ebberston, who saw the Mitsubishi Shogun before the collision or who witnessed the collision itself.