A Buckingham Palace spokeswoman confirmed Prince Philip was driving when the accident happened.
The Duke's car was in collision with another vehicle.
The female driver and female passenger in the car involved in a collision with a Land Rover driven by the Duke of Edinburgh were treated in hospital, Norfolk Police said.
Both drivers involved in the collision were breathalysed, as is force policy, and both provided negative readings, Norfolk Police said.
The force said: “Norfolk Police can confirm officers attended a collision on the A149 at Sandringham today.
“Officers were called to the scene shortly before 3pm after a Land Rover and Kia were involved in a collision.
“The male driver of the Land Rover was uninjured. The female driver of the Kia suffered cuts while the female passenger sustained an arm injury, both requiring hospital treatment.
“We can confirm both casualties from the Kia have been treated at the Queen Elizabeth Hospital in King’s Lynn and have since been discharged.
“The road remained open and both vehicles were recovered a short time later.”
A royal spokeswoman added: “[The Duke] saw a doctor as a precaution and the doctor confirmed he was not injured.”
The spokeswoman would not comment on who Philip’s passenger was, but it is likely the duke was travelling with his close protection officer.
Berneen Caney, 25, who witnessed the scene of the accident, said: “It appeared to be quite serious, there was a lot of glass over the road as well as debris, I saw one of the cars was quite badly damaged, as for the Range Rover, its windows were smashed.”
The support worker from King’s Lynn added: “By the time I passed by, the Range Rover had been tipped back up on its wheels.
“I didn’t see that much as I was more concerned the car in front of me was braking to turn off and that there was glass and debris all over the road.
“There was a lot of people there including police, and there was a paramedic there too.”
Luckily, the Duke avoided serious injury.
The Archbishop of York shared a message of support for the Duke of Edinburgh following the car accident.
John Sentamu tweeted: “Almighty God, the Fountain of all Goodness, We humbly beseech thee to bless Philip Duke of Edinburgh: Endue him with thy Holy Spirit; enrich him with thy Heavenly Grace; prosper him with all happiness; and bring him to thine everlasting kingdom, through Jesus Christ our Lord. Amen.”
An image from the scene of the crash published by local radio station KLFM 96.7 showed two cars by the side of the road, one on its side with a smashed windscreen and another a few yards away in bushes.