Greens senator Lidia Thorpe has resigned as the party’s deputy leader in the Senate.
The ABC revealed earlier on Thursday that Senator Thorpe “briefly dated” the ex-president of the Victorian Rebels outlaw motorcycle gang, Dean Martin, while sitting on a parliamentary law enforcement committee.
Senator Thorpe acknowledged she did not disclose the relationship to Mr Bandt.
Within an hour of the ABC's report, Mr Bandt called a press conference where he repeated that he was unaware of the matter until contacted by the ABC.
He said Senator Thorpe should have disclosed her connection to Mr Martin and the failure to do so showed a "significant lack of judgement".
"Senator Thorpe had an important role not only as our justice spokesperson but on the law enforcement committee," Mr Bandt said.
"Her friendship could be perceived as an issue given her work as a senator, especially on those committees.
"It was clear that this could be perceived as affecting her work."
Mr Bandt asked for Senator Thorpe’s resignation from the leadership team, and said it had been received.
In a separate statement, Senator Thorpe said she accepted she had "made mistakes" and had not "exercised good judgement".
Mr Bandt said the failure to disclose was "disappointing", but Senator Thorpe continued to "have a lot to offer this country and a lot to offer this parliament".
Prime Minister Anthony Albanese said the revelations concerned him.
"Australians are entitled to believe the oversight processes that are there in the parliament will be maintained in a way that ensures integrity and ensures that any information given there is kept in a confidential basis," Mr Albanese said.
He said Mr Bandt must explain what his office knew and what he knew about the undisclosed relationship.
A Department of Finance review into the culture of Senator Thorpe's office is underway, initiated following a complaint by one of her staff.
Senator Thorpe will remain a Victorian Greens senator.