Twenty-five players - thought to mostly be qualifiers - on board the flight from Doha to Melbourne must isolate in their room for 14 days.
Heather Watson is one of 47 players who were already quarantining and some are frustrated by the confinement.
Tournament organisers said the players were "already in quarantine hotels".
An Australian Open statement said: "One positive Covid-19 test has been returned from a passenger on a charter flight into Melbourne from Doha which arrived at 5.30am on 16 January.
"The passenger is not a member of the playing contingent and had tested negative before the flight.
"There were 58 passengers on the flight, including 25 players."
At least three players said they might not have gone to the tournament if the rules had been made clear to them.
Organisers said the rules were clear, and the event would begin as planned on 8 February.
Three other people tested positive for Covid on Saturday and one on Sunday. They had been on two chartered flights bringing players to the tournament.
France's Alexandre Muller, one of six qualifying lucky losers travelling as a reserve should anyone drop out of the main draw, tweeted the message he received to inform him he had to isolate.
Two-time winner Victoria Azarenka, 2016 champion Angelique Kerber, former US Open champion Sloane Stephens and Japan's former world number four Kei Nishikori are among those affected.
Emma Cassar, quarantine commissioner for the state of Victoria, said people in the hotels - including one player - were breaching lockdown rules by opening their doors to communicate with others on their floor.
All players taking part in the competition had to test negative before boarding flights and were then placed in designated Australian Open quarantine hotels in Melbourne and Adelaide.
Those who have not been confined to their rooms because of positive tests on their flights are allowed out for up to five hours a day to practise on court.
The first Grand Slam of the year had already been hit by the withdrawal of injured Roger Federer, while three-time major winner Andy Murray tested positive for the virus before departure so did not fly to Australia.