“He found her too needy and it just wasn’t working out,” the US publication cited a source close to the royal as saying.
Clarence House, the office of Harry’s father Prince Charles, declined to comment.
Britain’s Telegraph reported that the split may not be permanent.
“The relationship has certainly at least paused for a breather,” a “well-placed” source told the paper.
“It is virtually impossible to have a successful romance and relationship in the full glare of the world’s media,” they said, adding that it was “impossible to say” what the future held for the pair.
Harry’s brother Prince William split up with his future wife Katherine in 2007, but the pair were reunited several months later and married in 2011.
“Cressy” and Prince Harry, fourth in line for the British throne, were first spotted together in July 2012.
They were introduced by Princess Eugenie, Harry’s cousin, a friend of the 24-year-old beauty. The couple tried to keep their relationship out of the paparazzi spotlight.
In March, the two were seen in public twice in the span of a weekend, prompting the British press to speculate that things were getting serious.
They were photographed kissing at an event in London’s Wembley Arena, sparking rumours another royal wedding on the cards.
Two days later they were spotted at Twickenham stadium for a Six-Nations rugby match.
Bonas — the daughter of model Mary-Gaye Curzon and entrepreneur Jeffrey Bonas — works in marketing in London.