The picture, released as part of photographer John Scott's royal exhibition, which will go to auction later this month.
Scott was given unprecedented access to the Royals from the 1950s to the 1980s, and has a collection of over 4000 unseen photographs from that period.
Prince Harry's paternity has long been debated.
Conspiracy theorists often point to the fact that both Harry and Princess Diana's riding instructor James Hewitt have red hair, and also the fact that they look similar.
In 1986, two years after Prince Harry was born, Princess Diana started an affair with Hewitt, which lasted five years. Princess Diana herself admitted that she and Hewitt had an affair during a BBC Panorama program in 1995.
While Hewitt admitted in a later interview, 'It was never her intention to fall in love with me, and it was certainly not my intention to fall in love with Diana, but it happened because of the circumstances throwing us together.
'It's very difficult to say how physical she wanted the relationship to become. And I'm not going to suggest one way or the other whose fault it was, it developed and it was mutual.'
However, the rumours that Hewitt is Prince Harry's real father are quashed by the fact that Diana didn't meet the trainer until after Harry was born.
In 2017, Diana's butler Paul Burrell revealed on I'm A Celebrity...Get Me Out Of Here, 'I never heard any of the Royal Family discussing James Hewitt being Harry’s dad because we knew the truth. It’s something that’s been made up. It was just because Harry had red hair, but all the Spencers have red hair.'