Matters are said to have come to a head after Dr Edwards' interview with Mr Woodhouse some weeks ago.
In days before the interview, Mr Woodhouse had become embroiled in the controversy around businessman and National Party donor Donghua Liu and Dr Edwards asked a series of questions about the matter.
But some involved with the show, including producer James Meager, are said to have found his approach too aggressive.
Mr Meager has confirmed that as well as producing the show, he is Mr Woodhouse's campaign manager but refused to comment further.
However he told the Otago Daily Times yesterday that he "purposefully removed myself from the production of the Michael Woodhouse interview to remove any potential conflict of interest''.
The show would continue without Dr Edwards but will no longer be live-streamed on nzherald.co.nz.
Otago University spokeswoman Megan McPherson said Mr Meager "has declared his conflict of interest right from the start and that has been managed very professionally".
"He has removed himself from situations where there could be potential bias."
Dr Edwards this morning said "the issue is now one that the union is helping me deal with and I'm a position where I can't give any further comment."
Mr Woodhouse told the Herald he had no concerns about Dr Edwards' questions during the interview which were "direct and challenging, as I expect in an interview".
"I found them to be fair and balanced."
He was "aware that there are a range of people involved with political parties from both the left and the right who are part of the research and production team for Vote Chat".
"I don't believe that any of those memberships in any way influence the selection of the politicians who appear on the show or the substance of the interviews."
Labour's Dunedin South MP Clare Curran who has also appeared on the show said she didn't detect any bias from either Dr Edwards or the production crew.
However she also said she had been "concerned about the overt relationship between a political party and a show like that".
She raised that with Dr Edwards after her appearance.
"I do think that it's questionable. If they are trying to be credible ... then having somebody who's directly associated with a political party is problematic."