The car was a Range Rover and had been driven by 97-year-old Prince Philip.
Buckingham Palace said that the Duke was pulling out of a driveway and onto the A149 road, when the accident took place.
The crash caused the Range Rover to turn over. Eyewitnesses were able to help the Duke of Edinburgh out of the car. He was, according to the BBC's Nicholas Witchell, "conscious but very shocked and shaken."
The Duke of Edinburgh is now back at Sandringham House and has been treated by a doctor. He passed a breathalyzer test as did the driver of the other car.
Two other people in the crash were not seriously injured.