The booing happened during an awards ceremony after the men's final, when a tennis official referred to global vaccine efforts as a sign of optimism.
It comes just as Australia begins its national inoculation programme.
Deputy Prime Minister Michael McCormack called the crowd's behaviour "disgusting".
"I don't like booing at any event, and certainly any sporting event," he told reporters in Canberra on Monday.
"This vaccine is going to get our country back to some sort of pre-Covid normality," he said.
The men's number one player Novak Djokovic won the final against Russian Daniil Medvedev on Sunday.
Djokovic in the past has been criticised for appearing to have a a casual attitude towards virus-related restrictions and health measures.
Australia kicked off the first stage of its vaccine programme on Monday. Frontline, health and quarantine workers are in line to get the first of 60,000 Pfizer vaccine doses this week.
While the vaccine has broad support locally, it has also sparked protests. On Saturday, small crowds of anti-vaccination demonstrators marched in cities including Melbourne and Sydney to protest against its rollout.
In Melbourne, where the Australian Open was held, the crowd also booed mention of the Victorian state government when Tennis Australia chief Jayne Hrdlicka thanked authorities.
Last week, the government ordered the state's residents into a snap five-day lockdown amid fears of an outbreak. The tennis event was allowed to proceed and the virus did not spread.