Despite the setback in 1972,Larsson went on to become one of Sweden's most fearless campaigning journalists before achieving posthumous fame with his Millennium trilogy of crime novels featuring the enigmatic heroine Lisbeth Salander.
He died aged just 50 in 2004 before he could reap the benefits of his work. He suffered a heart attack after climbing seven flights of stairs because the office lift was broken.
Many feel the success of the novels overshadowed his achievements as a journalist and the letter, which he kept for 32 years, shows he had to battle even as a young man. It will be included with a one-off box set of his three novels to be sold at Sotheby's to raise money for Expo.
Christopher MacLehose, who discovered and published the novels after Larsson's death, said the family was asked for something that was a one-off. "This is a letter saying 'you are not good enough to be a journalist' to a man who went on to create a supremely creative, crusading magazine which fought against the worsening tide of extreme right thinking and activity in Sweden. He did things which no other Swedish journalist came anywhere near doing."
Larsson's brother, Joakim, told the Guardian he did not think his brother became bitter at the rejection but "of course he was not happy. He thought he would apply the next year but I don't think he ever did. For me, it is very important that the money goes to Expo, that was his magazine and it is a very important magazine – they need all the money they can get."
The letter, which also has a pencil doodle on the back, has an estimate of £8,000-£12,000. It will be sold alongside a leatherbound box set of his novels – The Girl with the Dragon Tattoo, The Girl Who Played with Fire and The Girl Who Kicked the Hornet's Nest – on 15 December.
Larsson put himself at considerable personal risk throughout his journalism career. He and his partner, Eva Gabrielsson, would sit in coffee shops facing in different directions, or taking different bus routes home, and one reason they did not marry - which has created problems since - is because their address would have been made public.
MacLehose said Larsson never stopped. "One of Larsson's great gifts, I've seen television footage of him, was staying calm in the teeth of lunatic, mouth-frothing frenzy – waiting for the storm to pass and then answering with the right answer."
The three books have sold more than 55m copies. The Swedes have made them into well-received films and the first Hollywood version of The Girl with the Dragon Tattoo, directed by David Fincher and starring Daniel Craig as the woman-magnet journalist Mikael Blomkvist, comes out this year.
MacLehose recalled first reading them and feeling he "couldn't not publish them", and thinks the 15 or so other publishers who turned them down, were daunted by their size. Plus, he said, there was a marketing orthodoxy, particularly in the US that said "you can't publish a dead person and if you make it worse by saying he was a dead Swede and you've got to pay for the translation".
The idea of the box set came from Mark Smith, CEO of Quercus books, which has the MacLehose imprint. Designed by British bookbinders Sangorski & Sutcliffe the books are bound in crushed black Morocco leather and interlock with silver studs: a representation of the sado-masochism of some of the books' male characters.
Because Larsson did not leave a will and never married Gabrielsson, the estate is in the hands of his father and brother, and the two sides are in a bitter dispute. Gabrielsson is campaigning for a change in the law and said in a Guardian interview this week: "People whose misery was private, who have lost everything to their dead partner's family overnight, they cheer me on and say: 'You are our voice as well. Please don't be silent.'"