The government will back the bid to the tune of A$1 million (597,140 pounds) initially with another A$4 million available if it looks like being successful.
The Australian women's national team, dubbed 'the Matildas', are currently ranked eighth and reached the World Cup quarter-finals for the third successive tournament in Canada in 2015.
"It's a great initiative. It's a great goal. And I'm excited to announce that the government will be backing the FFA's bid for Australia to host the 2023 Women's World Cup," Turnbull told reporters in Canberra.
"The Matildas are leaders on the international stage and they are wonderful role models in our community ... wouldn't it be fantastic to have the Matildas contesting a women's World Cup on home soil, here in Australia?"
Colombia, Japan, New Zealand and Thailand have all expressed interest in hosting the 2023 tournament but Australia's experience of successfully staging major sporting events and the government backing would put them among the favourites.
The 2000 Sydney Olympics, 2003 Rugby World Cup, soccer's 2015 Asian Cup, as well as the co-hosted 2015 cricket World Cup, all drew high praise for organisers.
"We set the bar, the highest level, in hosting great global sporting events," Turnbull said, adding: "A women's World Cup hosted in our back yard would inspire a new generation of women and girls right across Australia."
The government paid out A$46.5 million to back a Football Federation Australia bid to host the 2022 men's World Cup, which won just a solitary vote in a ballot that resulted in Qatar being handed the tournament.
"We are acutely aware that the previous bidding process for the 2022 men's World Cup was called into question with the most serious probity allegations," read a joint statement from the government and FFA announcing the bid.
"Our advice is that FIFA has reformed and is committed to an open and transparent bidding process."
The next women's World Cup takes place in France in 2019.
(Reporting by Nick Mulvenney and Colin Packham, editing by Peter Rutherford)
