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."