The comedian told The Guardian that he received a phone call from Douglas while he was complaining on air about an internet campaign skewing a listener poll of the greatest duets.
Jupitus said: "I started whining about this on air and getting crosser and crosser and then my mobile went and it was Lesley Douglas.
"She said, 'If you want to destroy 6 Music keep doing what you are doing on air now'. And I went, 'This is not a f**king 6 Music show, this is not what the station is supposed to be about'. I kind of lost it with her and hung up."
Jupitus left 6 Music in March 2007. Douglas herself resigned from the BBC in the aftermath of the broadcast of an obscene phone call from Russell Brand and Jonathan Ross to Andrew Sachs.
Talking about his five-year stint as breakfast DJ on the station, Jupitus added: "There were people at 6 who hated the fact I wouldn't play Coldplay records or Razorlight. But you can hear them on Radio 2, they are the biggest band in the world.
"Because a niche music station doesn't play Coldplay, is that a bad thing? They had a slogan at the beginning of 6 Music, 'We play what we like and nothing else'. I was playing a lot of s**t in the early days, that kind of faux indie stuff I can't bear.
"I remember thinking: that poster's lying. Now, after ten years of experience, it has struck a balance. You just have to listen to Lauren Laverne's show. There's a lot of great stuff in there, new and old."
Jupitus also revealed that he considered leaving BBC music comedy panel quiz Never Mind The Buzzcocks when it was being hosted by comedian Simon Amstell.