"The passengers who have been designated close contacts will be unable to access training and will undertake a standard 14-day quarantine period," a representative for COVID-19 Quarantine Victoria said.
In quarantine, players must train indoors, instead of being allowed out for five hours training per day, part of conditions that allowed the event to go ahead.
"Unfortunately we have been informed by the health authorities that two people on your flight AR7493 from LAX that arrived at 5.15am on Friday 15 January have returned positive COVID-19 PCR tests on arrival in Melbourne," said a message posted on Instagram by Mexico's Santiago Gonzalez, who is ranked 48 on the doubles circuit.
"From having 5 hours of training in a bubble to this ... (strict quarantine x 15 days). I will be showing you my workouts x Instagram (inside the room)," Uruguayan world number 68 Pablo Cuevas said on Twitter.
The news was first reported by The Age newspaper.
Australia has agreed to accept about 1,200 players, officials and staff on 15 flights for the major sporting event that is due to begin next month. Tennis officials were not immediately able to comment.
Other players cited by local media as likely to be on the flight included Tennys Sandgren, who was granted special permission to travel from Los Angeles late last week after testing positive for the new coronavirus, which he had previously had, and world 13 doubles player Victoria Azarenka of Belarus.
Scottish former world number one Andy Murray revealed he tested positive for COVID-19 last week but said he was in good health and still hoped to compete. American Madison Keys pulled out last week after she tested positive. urn:newsml:reuters.com:*:nL9N2IR004 urn:newsml:reuters.com:*:nL4N2JP3HI
The inbound infections came as Australia recorded a single locally acquired case, and as states began to relax travel bans on signs an outbreak in the northern state of Queensland has been contained.
The case, in western Sydney, is thought to be linked a known cluster in New South Wales, the most populous state, health officials said.
Australia has halved the number of returning travellers that it will accept, to lower the risk of highly infectious strains seeping into the community, as occurred at a site in Queensland two weeks ago.
Emirates Airline EMIRA.UL said Friday it would suspend flights between Dubai and Melbourne, Sydney and Brisbane by early next week until further notice.
Queensland has recorded two weeks since its latest hotel outbreak, fuelling hopes the spread has been contained. As a result, Victoria and South Australia states will reopen borders to the state by Sunday.
Australia, which logged 20 infections hotel quarantine overnight, has been one of the world's most successful nations in managing the coronavirus spread, with about 28,700 infections and 909 deaths.
(Reporting by Melanie Burton and Ian Ransom; Editing by William Mallard) ((email@example.com Twitter: @MelanieMetals; +613 9286 1421; Reuters Messaging: firstname.lastname@example.org))