The 48-year-old singer and actor Joshua Sasse, 28, announced their engagement earlier this year.
The couple subsequently vowed to postpone their nuptials until same-sex marriage becomes legal in Australia.
Dressed in "Say I Do Down Under" T-shirts at the Arias in Sydney, the pair urged the change to come next year.
"We're here to introduce a shining light in the Australian music industry," Minogue told the audience on Wednesday night.
"But we're also here to say thank you to everyone who has supported Josh's campaign for equality."
Sasse, who founded the "Say I Do Down Under" campaign, said: "This is more than a movement, this is people's lives and we want to say to every single member of the LGBT community that you are not alone.
"You have a voice and if we all stand together we can bring Australia back on the right side of history and make 2017 the year that we can all say 'I do' down under."
Australian pop star Sia also used the awards night to address the issue, sending a same-sex marriage campaigner to collect her award for best female artist.
The Australian government's plan to settle the same-sex marriage debate through a public vote early next year was blocked by the Senate two weeks ago.
Critics said a nationwide campaign would be expensive, unnecessary and unleash a torrent of homophobic rhetoric.
Sasse's "Say I Do Down Under" campaign, along with other lobby groups, is now pushing for parliament to change the law.
His campaign has attracted celebrity supporters including Chris Martin, Ellie Goulding and Sir Ian McKellen.
Kylie Minogue and her British fiancÃ© have called on Australia to legalise same-sex marriage in an appearance at the nation's top music awards.