Auckland City Council intervened after Mr Bennachie contacted Sandra Coney, chairwoman of the council's Parks and Heritage Forum.
Auckland City Council owns Big Day Out venue Mt Smart Stadium.
Big Day Out organisers could not be contacted for comment this evening.
Mr Bennachie told APNZ he had tried to listen to Odd Future's music, but turned it off promptly.
"I find it quite sickening. I don't like hate being propagated in ways like this. It's damaging to people, it's damaging to society.
"The messages in the songs are that LGBT people are immoral, evil, sick and worthless and therefore violence is an easy step for those who are already disposed towards violence.
"Too often gay men are targeted as objects of violence or ridicule in the streets and the perpetrators feel safe in targeting them because of the messages contained in hate music like this.''
It is not the first time an act has been pulled from the Big Day Out over homophobic views.
Performer Beenie Man was pulled from the 2010 event after gay rights groups expressed outrage at his invitation due to lyrics such as: "I'm dreaming of a new Jamaica, come to execute all the gays''.
Leader of Odd Future, Tyler the Creator, has previously denied accusations his lyrics are homophobic.
"I'm not homophobic,'' he told magazine NME.
"I just think `faggot' hits and hurts people. It hits. And `gay' just means you're stupid. I don't know, we don't think about it, we're just kids. We don't think about that shit. But I don't hate gay people. I don't want anyone to think I'm homophobic.''