They include connections of the race winner Verry Elleegant, reports say.
The function was attended by 100 guests and pictures posted on social media showed people drinking from the cup during the event last Tuesday evening.
People could be seen dancing, mingling and not wearing masks.
The owner of the restaurant, Chris Lucas, says there was rapid antigen testing on the night of the event and no positive tests were recorded.
Melbourne businessman Brae Sokolski and an owner of Verry Elleegant told 3AW radio he was cleared of the virus after testing.
Other guests included former AFL great Wayne Carey and ex-Australian cricket captain Ricky Ponting.
Victorian Chamber Chief Executive Paul Guerra said everyone at the venue was double vaccinated and warned there has to be an expectation of some COVID-19 circulating in the community after opening up.
“We are perhaps seeing that out of the party but it’s contained so far and certainly they have done the right thing and gone and get tested,” he told Today.
Racing Victoria is asking all racing participants who attended the function to get tested as a precaution.
The Victorian Department of Health is now investigating.
Just two COVID-19 cases were linked to Melbourne Cup Day last Tuesday, when 10,000 people flocked to Flemington Racecourse.