Christine Forster last week declared her intention to put her hand up for Wentworth, after being encouraged by her brother and several party members.
But the City of Sydney councillor is now pulling out after her campaign became the focus of suggestions “that it was a proxy for division within the Liberal party”.
“That is not the case, but to avoid any such perception, I will be standing aside and giving my full support to the successful candidate,” she posted on Facebook on Monday.
“I remain committed to doing everything I can to ensure we defeat Labor in the coming battles.”
Former prime minister Mr Turnbull formally resigned on Friday. A by-election date is still to be set but it could be before October 6.
Meanwhile, the former Liberal MP for Wentworth Peter King, who lost preselection to Mr Turnbull in 2004, has confirmed he will try again.
“I’m nominating for the Liberal party,” he told Sydney radio 2GB on Monday.
King added it was his “melancholy duty to put the national interest first before ego”.
The other Liberal preselection candidates are Business Council of Australia executive director and same-sex marriage campaigner Andrew Bragg and Australia’s former ambassador to Israel Dave Sharma.
Labor is fielding financial analyst and Tamarama Surf Life Saving Club president Tim Murray, who’s already got the backing of Mr Turnbull’s son Alex Turnbull.
Sydney business owner and City of Sydney councillor Angela Vithoulkas is standing as an independent.
Another City of Sydney councillor – independent Kerryn Phelps – is considering whether to stand or not.
Make your contribution to independent news
A donation of any size to InDaily goes directly to helping our journalists uncover the facts. South Australia needs more than one voice to guide it forward, and we’d truly appreciate your contribution. Please click below to donate to InDaily.