A palace spokeswoman told AFP that the duke was driving near the monarch's Sandringham Estate when the crash occurred but declined to confirm that it overturned in the incident.
"The Duke of Edinburgh was involved in a road traffic accident with another vehicle this afternoon," the palace said in a statement.
"The Duke was not injured. The accident took place close to the Sandringham Estate. Local police attended the scene."
The spokeswoman said he saw a doctor "as a precaution" who confirmed he was not hurt.
Norfolk Police said in an update Thursday night that, in accordance with policy in collisions, it breathalysed both drivers.
"We can confirm both drivers were breath tested and provided negative readings," the force added.
It said officers were called to the estate shortly before 3:00 p.m. (1500 GMT) "after a Landrover and Kia were involved in a collision".
"The male driver of the Landrover was uninjured," it added.
"The female driver of the Kia suffered cuts while the female passenger sustained an arm injury, both requiring hospital treatment".
They were later discharged from a local hospital, police said.
The BBC reported that Prince Philip's vehicle flipped on its side after pulling out of a Sandringham driveway onto a main road and colliding with the other car.
Eyewitnesses told the British broadcaster they helped the duke out of the vehicle and he was conscious "but very, very shocked and shaken".
An image from the accident scene published by a local radio station 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.
The Press Association reported a passenger in the duke's vehicle was likely his close protection officer.
- carriage driving -
The royal couple spend most of the winter at the residence in Norfolk, an English county northeast of London, which continues to operate as a sporting estate.
Philip, known for his forthright manner and off-colour jokes, formally retired from public life in 2017.
He has been seen behind the wheel on numerous occasions over the decade, including with world leaders and dignitaries as his passengers.
In 2016, alongside the Queen he drove former US President Barack Obama and his wife Michelle around Windsor Castle in a Range Rover after they landed nearby in the presidential helicopter.
Meanwhile the duke continued to compete in demanding carriage driving competitions into his 80s, and has previously pulled muscles in his back while driving his horse-drawn carriage.
After announcing his retirement, Philip described in an interview how he took up carriage driving when he gave up polo aged 50, helping to establish it as a sport in subsequent years.
Born a prince of Greece and Denmark, he married then princess Elizabeth on November 20, 1947 at Westminster Abbey in London.
On their golden wedding anniversary in 1997, she said of him: "He has, quite simply, been my strength and stay all these years."