Mr Djokovic believed he was exempt from needing to be vaccinated as he had been infected with COVID-19 back in December.
According to the terms of the ban he will not be allowed to enter Australia for the next three years.
But when asked if the 34-year-old tennis champion would be able to compete in the Australian Open next year, Mr Hawke said: “The future for Mr Djokovic is his to decide on how he conducts himself and what he does internationally.
“The Australian government has no further role in what he chooses to do.”
Mr Hawke said the possibility of the ban being waived was “open to consideration”, however, it seems certain that Mr Djokovic would need to be vaccinated for that to happen.
Mr Djokovic’s stance on the COVID-19 vaccine has meant he may not be able to play in any international tennis championships this year.
He said to the BBC: ”I was never against vaccination, but I’ve always supported the freedom to choose what you put in your body.
“Because the principles of decision making on my body are more important than any title or anything else.
He said: “I never used my status to get into Australia by force or to do anything in this entire process.
“The email I received, that was sent to all athletes, we were following the rules and when there was a possibility for a medical exemption, we were using that.
“I put forward my PCR test and that I had the right antibodies at the time and that was accepted by two independent Australian medicals, anonymously it is important to clarify.”