The deputy chief of the Liberal Party, Bishop had put her hand up to be one of three candidates to replace former prime minister Malcolm Turnbull in Friday's leadership challenge, but received minimal support from colleagues even as opinion polls pointed to her popularity among voters.
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Her departure has raised questions about whether she fell victim to party politics and a perceived glass ceiling for women in Canberra.
"I will be resigning from my cabinet position as Minister for Foreign Affairs", Bishop said in a statement, signalling her intention to remain on the backbench.
A moderate, she reportedly garnered only 11 votes out of 85 in the leadership ballot--significantly lower than the two other rightwing challengers, coup instigator Home Affairs Minister Peter Dutton and Treasurer Scott Morrison.
A leaked WhatsApp chat between some Liberal members, revealed by the Australian Broadcasting Corporation Sunday, showed them pushing against voting for Bishop as a tactic to back Morrison, who finally emerged as the winner.
Australia has endured a turbulent period in politics that has seen six changes in the top job in 11 years.
The chaos has highlighted not just the infighting within the two major parties--Liberals and Labor--but also how politicians and the electorate view women in power.
One of the casualties was Labor's Julia Gillard, Australia's first female leader, who constantly battled misogyny and made international headlines for her fiery rebuttal of then Liberal opposition leader Tony Abbott in parliament in 2012.
Bishop has been candid about her experiences as the only woman among 18 men in cabinet after Abbott won national elections in 2013.
"It was pretty lonely," the former lawyer said last year, adding that she would suggest ideas which were ignored until copied by her male colleagues.
The male colleagues would suggest "exactly my idea, exactly my initiative...and the others would say, 'brilliant, what a genius idea!'", she said, putting down the behaviour to an "unconscious bias".
"It's almost a deafness that we still see in Australian society," she said.
A trailblazer who was Australia's first female foreign minister and the Liberals' first female deputy leader, the 62-year-old was hailed by her peers Sunday.
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Turnbull tweeted that she was "an inspiring role model for women here and around the world".
Her Labor counterpart Penny Wong praised her "tireless work ethic", adding that her "commitment to standing up for Australia both here and abroad has never been in question".
Renowned for her steely gaze dubbed the "death stare", Bishop's highlights as foreign minister include her strong condemnation of Russia's role in the shooting down of Malaysia Airlines MH17 in 2014.
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