Bankstown MP Tania Mihailuk used parliamentary privilege to air her concerns about the integrity of Canterbury-Bankstown mayor Khal Asfour late on Tuesday night.
She linked the potential future upper house MP to disgraced former Labor minister and party powerbroker Eddie Obeid.
Mr Minns told 2GB on Friday morning Ms Mihailuk had been ejected from the inner circle of the opposition.
He told Ms Mihailuk she cannot be in the shadow cabinet while launching political attacks by parliamentary privilege.
"I haven't heard back from her about those conditions, so I've come to the conclusion, reluctantly, that she can't stay in the shadow cabinet and abide by those conditions," Mr Minns said.
"She can't stay if she can't agree to these terms and it looks to me like right now, she can't agree to the terms."
Mr Asfour asked the Independent Commission Against Corruption to review Ms Mihailuk's "outrageous and unsubstantiated claims".
"She has used parliamentary privilege to launch a cowardly attack on me and my family and I call on her to produce evidence of any wrongdoing," he said.
Mr Asfour was recently selected as a potential candidate for the Labor upper house ticket at the March election, one of five right-faction Labor hopefuls.
Ms Mihailuk is one of three south-west Sydney Labor MPs fighting over two seats in the lead-up to the election.
Jihad Dib's seat of Lakemba is being abolished and largely absorbed into Bankstown, leading to a three-way preselection battle for Ms Mihailuk's seat and Guy Zangari's nearby Fairfield.
Ms Mihailuk was the subject of bullying claims last month, which she dismissed as "an internal stitch-up".
"There are people who want my seat and people who want me out of politics," she told 2GB.
Upper house Labor veteran Walt Secord also stepped down last month after bullying claims.
Labor's candidates are expected to be finalised following a conference next month.
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