The suggestion by Sooty creator Harry Corbett caused a furore in the press, which claimed it would "introduce sex into a children's programme".
The show's producer and a BBC governor were against Sooty having a girlfriend.
BBC DG Hugh Carlton Greene stepped in to allow panda Soo's introduction.
Matthew Corbett, Harry's son, told the documentary: "My father was called into the head office and the director general of the BBC said he had made a decision."
He said Greene had ruled that Sooty having a female friend "was to be allowed - but they must never touch".
So Soo was introduced in 1965 - originally voiced by Harry Corbett's wife Marjorie - and she has been at Sooty's side ever since.
The documentary, titled Sooty Ungloved, will have its world premiere in Guiseley, Yorkshire, on Saturday, with profits from the screening going towards providing a defibrillator for the area.
Corbett and his family lived in the town for 35 years. He and the puppet found fame on TV in the early 1950s.
When Corbett suggested introducing a female character in the 1960s, the show's producer Trevor Hill dismissed the idea "on the grounds that sex would be creeping into the programme", according to a letter written by Corbett in 1965.
The tabloid press picked up on the disagreement, causing a row between Corbett and Grahame Miller, the BBC's head of north regional programmes.
Miller accused Corbett of orchestrating a campaign in the press for Sooty to be allowed a girlfriend, letters from the BBC archive reveal.
As a result, he told Corbett the BBC was prepared to "hold up the contractual negotiations which are in train" and "urgently review the future of the Sooty series in BBC Television".
One of the BBC governors, Dame Anne Goodwin, was also strongly opposed to Sooty having a female friend.
In May 1965, Hill wrote to Miller: "I was left in no doubt as to her feelings in this matter!
"DG, however, said to me, 'I think you are wrong not to let Sooty have his girlfriend!'"
The Sooty Show was cancelled by the BBC two years later, however, before being picked up by ITV.
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The idea to introduce a female puppet to Sooty's children's TV show in the 1960s was so controversial that the BBC director general had to intervene, a new documentary has revealed.