"Is there any one of the Royal Family who wants to be king or queen? I don't think so," he told Newsweek.
And he said the royals were doing it "for the greater good of the people".
The prince also spoke about walking in the funeral procession for his mother, Princess Diana, when he was 12, saying no child "should be asked to do that".
In 1997, Harry joined his father, the Prince of Wales, grandfather, the Duke of Edinburgh, 15-year-old brother, the Duke of Cambridge, and uncle, Earl Spencer, in the procession through the streets of London.
Harry, who recently said he had received counselling to cope with the death of his mother in a car crash in Paris, said: "My mother had just died, and I had to walk a long way behind her coffin, surrounded by thousands of people watching me while millions more did on television.
"I don't think any child should be asked to do that, under any circumstances. I don't think it would happen today."
The Prince also talked about the role he and his brother are taking in what he called "modernising the monarchy".
He also paid tribute to his "remarkable" grandmother for letting the younger royals do things their own way.
"The Queen has been fantastic in letting us choose," he says. "She tells us to take our time and really think things through."