Thursday's play at the six warm-up events at Melbourne Park has been cancelled as a result.
But Victoria Premier Daniel Andrews said: "At this stage there is no impact on the tournament proper."
Players will be free to return to competition after a negative test.
"We will work with everyone involved to facilitate testing as quickly as possible," said Australian Open organisers.
The Grand Slam tournament, which was pushed back by three weeks to enable players to quarantine, starts on Monday.