The party's co-deputy Sam Hibbins said a "short relationship ended some time ago, but it does breach our party room rules".
"I've had a consensual relationship with a staff member from my office," he said in a Facebook post.
"I recognise this was a significant error of judgement and understand the distress this has caused."
Sam Hibbins has quit the Greens after admitting he breached party rules.
Mr Hibbins said he was aware it was a distraction from his work with the Greens but he will "remain committed to serving (his) electorate of Prahran".
He will become an independent MP.Â
"At a time when life is so difficult for so many, when people are struggling and are already disengaged from politics, I know something like this will shake people's trust in politicians and politics even further.
"I deeply regret what has happened.
"I have made a very human mistake, but I am working to find the best way forward."
State Greens leader Ellen Sandell has called a press conference to address what she described as "serious allegations" about the Prahran MP.
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