"It licenses the press to investigate politicians' private lives", said Tom Switzer, the executive director of the Center for Independent Studies think tank who had sought Liberal Party endorsement for federal office.
Mr Joyce emphasised that standing down was aimed at protecting his new partner who is due to have their baby in April, as well as his estranged wife and daughters.
The Deputy PM said there has been a "litany of allegations" none of which have been sustained.
Before news of the scandal broke this year, Joyce, who was born in Australia, had been attempting to rebuild his reputation, damaged when he was ruled ineligible to remain Parliament after discovering he was also a citizen of New Zealand because his father was born here.
Joyce was besieged with scandals recently, including the revelation that he and his former staffer, Vikki Campion, were expecting a son together, as well as the new sexual harassment allegation against him, which he strongly denies.
Joyce had not directly told Prime Minister Malcolm Turnbull he is resigning but he said he spoke to Mathias Cormann, who is acting in the role while Turnbull is overseas.
Nick Economou, senior lecturer in Australian politics at Monash University in Melbourne, said it would have been impossible for both Mr Turnbull and Mr Joyce to return to parliament next week after they fell out.
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The ABC understands the complaint, made by a West Australian woman, is "serious" and relates to an allegation of sexual harassment. This was the question people turned to social media to answer as Barnaby Joyce began his resignation speech this afternoon.
Mr Turnbull explained that Mr Joyce was taking leave to consider his future. As well as deputy prime minister, he was minister for infrastructure and transport.
Joyce, however, said that while he will exit the Cabinet, he will not resign from the Parliament. So "I'll have other things on my mind".
The favourite to replace Joyce as leader is Michael McCormack, a junior minister from New South Wales.
But Mr Turnbull was effectively unable to sack Mr Joyce, whose position as party leader and Deputy Prime Minister is decided by National MPs.
Barnaby Joyce, the leader of the rural-based Nationals Party, told reporters that a sexual harassment complaint against him that emerged in the media the previous day had convinced him that his position was politically untenable.
Now, Mr Joyce faces a formal leadership challenge with a possible showdown next Monday after a Nationals MP announced he would move a resolution ousting Mr Joyce as party leader. He is minister for veterans' affairs and minister for defence personnel.
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