The duke emerged unharmed but two people in another auto were injured in the crash that occurred Thursday when the duke was driving near the Sandringham Estate, according to police and Buckingham Palace.
A nine-month-old baby who was in the back seat of the other auto, a Kia hatchback, was also uninjured, while one woman in the vehicle broke her wrist and the other cut her knee, local police said.
Eyewitnesses who helped the duke out of his vehicle said he was conscious "but very, very shocked and shaken".
The duke was "obviously shaken" but managed to stand up and ask how those involved in the crash were, he said.
There have been suggestions Prince Philip was travelling with a passenger, most likely his close protection officer.
Buckingham Palace said Philip, 97, was checked by a doctor after the accident and determined to be fine.
Norfolk County Council is due to discuss reducing the speed limit on the road from 60 miles per hour (96 km/h) to 50 miles per hour (80 km/h) and installing safety cameras.
Norfolk Police said, in accordance with policy in collisions, it breathalyzed both drivers.
A source tells BAZAAR.com that Prince Philip was at the wheel when the accident happened on a public road.
Norfolk Police said two women - the driver and passenger of a Kia - required hospital treatment but were later discharged.
The eyewitnesses said they helped the duke out of the vehicle.
The Prince was reportedly turning onto a main road when he was "T-boned", with his Land Rover flipping onto the driver's side.
A palace spokeswoman said: "On doctor's advice, the Duke of Edinburgh visited the Queen Elizabeth Hospital in King's Lynn this morning for a precautionary check-up".
A spokesperson for the police force has said: "Norfolk Police can confirm officers attended a collision on the A149 at Sandringham today".
Currently, British drivers have to reapply for their licence at the age of 70, and every three years thereafter, by self-certifying their sight is good enough to read a numberplate at 20 metres, and that they have no medical condition that prevents them from driving. "It was a horrendous accident and it's just unbelievable that people weren't seriously injured".
Both the Duke of Edinburgh and driver of the Kia were breathalysed, with both readings coming back as negative.
Philip, known for his forthright manner and off-colour jokes, retired from public life in 2017 and underwent a hip replacement operation last April.