Jamie Briggs was forced to stand down as Minister for Cities and Built Environment after the woman raised questions about his behaviour during the late-night outing.
Briggs would not elaborate on what occurred at the crowded bar after a dinner with his chief-of-staff and the woman, saying only that nothing illegal had been alleged or had occurred.
"At no point was it my intention to act inappropriately. This was an error of professional judgement," he said.
The Adelaide Advertiser said it understood the woman had been told by Briggs that she had "piercing eyes", and that he put his arm around her and later kissed her on the cheek as they left.
Briggs said he believed the evening was an "informal" occasion but admitted that, on reflection, he had not met the high standards of a minister.
The 38-year-old representative from South Australia prompted news stories in September when he injured his knee during a raucous farewell party for then prime minister Tony Abbott.
"We were mucking around, put it that way," he told the Australian Broadcasting Corporation at the time.
Prime Minister Malcolm Turnbull, who ousted Abbott in a leadership coup, said Briggs' conduct "fell short" of the standard required.
"After being invited to reflect on his position, he offered his resignation which I have accepted," Turnbull said in a statement, adding that Environment Minister Greg Hunt would assume Briggs' responsibilities.
Turnbull also revealed that another minister, Mal Brough, would stand aside as Special Minister of State and for Defence Materiel and Science pending a police inquiry.
Brough offered his resignation amid an investigation into his role in the downfall of the former speaker of parliament. He denies any wrongdoing.
Both Briggs and Brough will remain in parliament, but the loss of their portfolios paves the way for a ministerial reshuffle.
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