Four days later, however, the waters were muddied again with a leaked email from the Women's Tennis Association (WTA) telling players that unvaccinated athletes would still be welcome if they were prepared to do a 14-day quarantine.
Hawke's office has declined to comment on the WTA's letter but other officials have since undermined the minister's statement, saying that the issue is far from settled.
"It is not my call as to whether they are allowed into the country but if they are, we will manage that risk," Daniel Andrews, who runs Victoria's state government and is vehemently opposed to entry for the unvaccinated, said on Tuesday.
What that means for Djokovic and his bid for a record 21st Grand Slam title remains to be seen.
The Serbian world number one has declined to discuss his vaccination status and said last week he might not play at Melbourne Park, "things being as they are".
His absence would rob the tournament of arguably its biggest name, while leaving the record bid in limbo.
An "abundance of caution" has been Australia's mantra through the pandemic with the country's borders effectively sealed for 18 months.
Melbourne, the country's second-largest city and host of the Australian Open, has been locked down six times.
The sixth lockdown ended last Friday but only for the vaccinated 70% of adults. The unvaccinated remain banned from sporting events, bars and restaurants, and could remain so well into 2022.
Professional athletes, meanwhile, are under a vaccine mandate in Victoria which also covers coaches, officials, media and other staff involved in elite competition.
That means tennis players might well be the only unvaccinated cohort at the Australian Open, where ballkids, fans and umpires will need proof of vaccination.
Such a scenario has been viewed dimly by some fans and media pundits, who have urged organisers Tennis Australia and the government to take a stand.
"Even if that means game, set and match for world number one Novak Djokovic. It’s double vax or default," Greg Baum wrote in Melbourne newspaper The Age.
Tennis Australia (TA) has made no indication it will take such a step, saying only that it is working with authorities.
"We are optimistic that we can hold the Australian Open as close to pre-pandemic conditions as possible," TA said in a statement on Monday.
The stakes are high not just for 34-year-old Djokovic -- a significant proportion of players remain unvaccinated, although the uptake is growing.
An Australian Open missing a number of top players would be a concern for organisers, who spent tens of millions of dollars on biosecurity for the last edition in February.
Those special arrangements for players proved controversial in the lead-up to the tournament, with Djokovic among a privileged group put up in luxury accommodation in Adelaide.
Those conditions were in stark contrast to the spartan rooms allocated to normal Australians for hotel quarantine.
Djokovic was then pilloried by local media for passing on a list of requests to make quarantine easier for players.
For TA, the issue of vaccinations is a delicate balancing act.
They are desperate to ensure Djokovic's participation in a strong field, while at the same time avoiding a public relations disaster if they are perceived to have secured a special deal for the unvaccinated.
(Reporting by Ian Ransom in Melbourne; Editing by Peter Rutherford)