Buckingham Palace said the 97-year-old drove a Range Rover when the accident involved another vehicle.
Two people in the second vehicle were treated for minor injuries, reported a local newspaper.
Pictures from the scene seem to show the Duke's Range Rover resting on his side.
After the collision, Philip saw a doctor at the Queen's Sandringham Estate nearby in Norfolk, where he and the monarch live.
Archbishop of York, John Sentamu, offered a prayer to Philip on Twitter after the reports arose from the crash.
His retirement came more than five years after Buckingham Palace originally said he would begin to scalter his workload back even though he was eager to continue many of his duties.