The Serbian is the top-ranked player in the world and could move clear of Rafael Nadal and Roger Federer for grand slam titles if he can claim his 21st at Melbourne Park.
However, Hawke's comments regarding vaccination requirements cast doubts over Djokovic's participation, with the 34-year-old previously declining to reveal his vaccination status.
"You'll need to be double vaccinated to visit Australia," Hawke said to Australian Broadcasting Corporation radio. "That's a universal application, not just to tennis players. I mean that every visitor to Australia will need to be double vaccinated.
"I don't have a message to Novak. I have a message to everybody that wishes to visit Australia. He'll need to be double vaccinated."
With recent reports suggesting that over a third of professional players have yet to be fully vaccinated, a significant number could be denied the chance to play in the opening grand slam of 2022.
The men's ATP and women's WTA tours have attempted to encourage players with reservations to get the vaccine, and Tennis Australia explained that it was working with government authorities regarding conditions for the tournament.
"Our understanding is that the details around international visitors entering the country are yet to be decided and we hope to have more information soon," Tennis Australia said in a statement.
Australia's health minister Greg Hunt defended the ruling, explaining that the decision had been taken with the safety of the country's citizens in mind.
"The [rules] apply to everyone without fear or favour," Hunt said. "It doesn't matter whether you are number one in the world or you are anything else."
Djokovic, who withdrew from the Indian Wells Masters this month, has won nine of his majors at the Australian Open.