Footage from the party showed people embracing, dancing and shaking hands as they celebrated Verry Elleegant's win.
Co-owner Brae Sokolski told a Melbourne radio station he had tested negative.
A Victorian health department spokesman said restaurants were generally not considered "high-risk" for coronavirus transmission because everyone who enters them have to be vaccinated, and other Covid-19 safe measures are in place as well.
"Investigations are currently underway into Covid-19 exposure at Society restaurant," the spokesman said.
"If anyone has Covid-19 symptoms, they should get tested as soon as possible. Stay alert for updates as details of exposure sites are subject to change based on new information."
There were 1069 new local cases, 10 deaths, and 579 Covid-19 patients in Victorian hospitals as of Tuesday morning.
Kheir has been contacted for comment.