Philip, 97, was not injured in the crash on Thursday afternoon, Buckingham Palace said.
Norfolk Police said officers were called to the Sandringham Estate shortly before 3pm “following reports of a collision involving two cars”.
A spokesman added that police and ambulance crews attended and two people in one of the vehicles suffered minor injuries.
A Buckingham Palace spokeswoman confirmed the duke was driving when the accident happened.
She added: “He saw a doctor as a precaution and the doctor confirmed he was not injured.”
Images have emerged on social media of a Land Rover Freelander, said to be the Duke’s, having rolled on its side following the incident.
The spokeswoman would not comment on who Philip’s passenger was but it is likely the duke was travelling with his close protection officer.
The duke is no stranger to the driving seat, and was seen with very famous passengers in a Range Rover in 2016.
Philip showed the former US President Barack Obama and his wife Michelle the personal touch when he drove them and the Queen to Windsor Castle after the Marine One presidential helicopter landed close to the monarch’s Berkshire home during their visit to the UK in April 2016.
Even in his 80s, the duke continued to compete in demanding carriage driving competitions, and has previously pulled muscles in his back while driving his horse-drawn carriage.
In 2017, he joked how the rough and tumble of carriage driving left his “Balmoral dog cart” smashed up regularly.
In his first interview since he announced his retirement, Philip told how he took up the sport of carriage driving when he gave up polo aged 50.
He was instrumental in helping to establish the sport and took part well into his 80s, but gave up competitions some years ago.
Philip retired from official royal engagements in August 2017.
The duke had previously stepped down from his public duties but on occasion does attend events with the Queen.
Prince Philip retired from royal engagements in 2017 after more than 65 years supporting the Queen in her role as head of state, and attending events connected to his own charities and organisations.