NSW Labor secretary Sam Dastyari, convenor of the right Centre Unity faction, has described the Greens as "extremists not unlike One Nation".
Mr Dastyari told News Ltd the ALP must stop treating the Greens "like they are part of our family" and consider preferencing them last in seats where it was "in the Labor party's interest to do so".
He is preparing to move a motion at the state party conference next weekend calling for Labor to "no longer provide the Greens party automatic preferential treatment in any future preference negotiations".
Senator Milne said the "outburst" by Mr Dastyari demonstrated an attack on Labor's base.
Already incensed by Victorian Labor's decision to preference Family First ahead of the Greens in the state by-election in the seat of Melbourne, Senator Milne vented her anger on Saturday.
"Labor party people across the country will be horrified to think that if they vote for Labor they don't know if they will be electing a coalition person or a Family First person," she told reporters in Adelaide.
"What it shows is the faceless men in the Labor party do not have any principle any more, or any idea of what Labor stands for other than winning office.
"It's not about policy; it's not about the best interests of the country."
The Greens struck a deal with Prime Minister Julia Gillard in 2010 to form minority government when the federal election delivered a hung parliament.
Senator Milne was crucial in the negotiations which helped deliver the Greens a price on carbon, which Ms Gillard had rejected ahead of the poll.
The Greens leader said NSW Labor was prepared to advance the cause of the coalition and Family First, with a morphed state between Labor and coalition policies.
Mr Abbott said the move by the NSW faction was telling.
"It's clear who is really in charge of the Labor party - the faceless men, whether it's deciding their preference strategy ... whether it's deciding who the leader is," he told reporters in Brisbane.
"The faceless men are ultimately calling the shots."
Mr Dastyari leads the faction which counted former senator Mark Arbib among its numbers.
Mr Arbib was known as one of the so-called faceless men, alongside Victorian Labor MP and minister Bill Shorten, who helped depose Kevin Rudd in 2010 and replace him with Ms Gillard.
Mr Dastyari is hoping other ALP state branches will follow the NSW move.
Senator Milne said Mr Dastyari had shown the ALP wanted to get involved with extreme parties like the conservative Family First.
"That's where the extremism is in Australian politics and the Greens actually represent mainstream values and mainstream opinion," she said.
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