Prince Harry, Meghan and his mother were involved in a “near catastrophic car chase” involving the paparazzi, according to the prince’s spokesman.
The incident happened after the Duke and Duchess of Sussex attended an awards ceremony in New York on Tuesday.
In a statement, the prince’s spokesman said the “relentless pursuit” lasted more than two hours.
This led to clashes with other drivers, pedestrians and police officers on the road.
The BBC was unable to independently verify details of the incident.
“While being a public figure comes with public interest, it should never come at the cost of anyone’s safety,” the spokesperson said.
“The dissemination of these images, given the means by which they were obtained, encourages a highly invasive practice that is dangerous for all involved.”
The New York Police Department (NYPD) did not immediately confirm knowledge of the incident.
The awards ceremony – the Ms Foundation Women of Vision Awards – will be the couple’s first public appearance together since the King’s coronation earlier this month.
They were accompanied by Meghan’s mother, Doria Ragland.
Prince Harry’s mother, Princess Diana, was killed in a car crash in Paris in 1997 after being chased by photographers.
In an interview with the BBC for the documentary “Diana, 7 Days,” Prince Harry referred to the paparazzi who constantly hound his mother as “a pack of dogs.” “Every time she goes out there’s a crowd waiting for her,” he said. “I mean a pack of dogs, chasing her, chasing her, harassing her, calling her names, spitting on her, trying to get a reaction, trying to get that photo of her lashing out.”
Earlier this week, a lawyer representing Prince Harry told a London court that he should be allowed to challenge the government’s decision to deny him the ability to pay for police protection while in the UK.