Hundreds of party members cast their ballots in the Sydney shire on Monday night for the candidate they thought was best to replace former prime minister Scott Morrison as his resignation triggers another by-election.
Mr Kennedy beat Sutherland Shire Mayor Carmelo Pesce 158 votes to 90 in the first round.
Former prime minister Scott Morrison's resignation as member for Cook has triggered a by-election. (Lukas Coch/AAP PHOTOS)
War widow Gwen Cherne, the only woman to contest the ballot, was third with 35 votes and Ben Britton fourth with 13.
Victorian MP Keith Wolahan said his party needed more women, particularly in the House.
"What we have to do is to feed through members and pre-selection candidates who will then succeed, and there are so many talented women in the party who are doing that, who are putting their hands up now," he told ABC's Q and A on Monday night.
Mr Kennedy is a partner of consulting firm Banksia after leaving McKinsey, according to his LinkedIn profile.
He contested John Howard's former seat of Bennelong at the 2022 federal election but came up short against Labor's Jerome Laxale after an almost eight per cent swing against the Liberals.
Cook is a safe Liberal seat - Mr Morrison holds it with a more than 12 per cent margin on 55 per cent of the primary vote.
The former prime minister experienced a more than eight per cent drop in his primary vote at the last election.
Labor is yet to determine whether it will formally run a candidate in Cook.
Prime Minister Anthony Albanese said Cook was not a seat Labor was expected to win.
He criticised the Liberals for failing to pre-select more women.
"I noticed that the Liberal Party have the opportunity to finally select a woman candidate," he told ABC Radio ahead of Monday's vote.
Anthony Albanese, pictured with MP Jodie Belyea, says Labor is not expected to win the seat of Cook. (Joel Carrett/AAP PHOTOS)
"But we'll wait and see whether they actually do or whether it's yet another bloke sitting behind Peter Dutton just saying no to everything."
The by-election will be the second this year following Saturday's poll in Dunkley, which was triggered by the death of Labor MP Peta Murphy in December.
Jodie Belyea retained the Victorian seat for Labor, fighting off a 3.5 per cent swing to the Liberals on a two-party preferred basis.
Labor's primary vote increased slightly, while the Liberals recorded a 6.5 per cent uptick.
One Nation and Clive Palmer's United Australia Party did not run candidates.
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