It is the latest blow to preparations for the year's first Grand Slam in Melbourne — which has already be delayed by three weeks due to the pandemic.
A total of nine people have tested positive while in quarantine ahead of the event in Melbourne, but two cases were deemed to be historical infections on Tuesday.
In good news for players in lockdown, there were suggestions that some may be allowed to leave their rooms for practice before the 14-day hard quarantine period.
Kyrgios joined a wave of criticism of the Serb for reportedly issuing a list of demands for quarantined players who have arrived in Melbourne and Adelaide on chartered flights.
Australian Open 2021: Bianca Andreescu coach Sylvain Bruneau tests positive for COVID-19 upon arrival in Melbourne
In all, 47 players have been barred from practising in Melbourne after it was revealed that passengers on two charter flights — one from Abu Dhabi and one from Los Angeles — tested positive.
Australian Open 2021: Forty-seven players barred from practising after 'close contact' with COVID-19 positive individuals
Two-time Australian Open champion Victoria Azarenka was reported by local media to be among a group of players set to be under the strictest quarantine for two weeks.
The charters and the early arrivals are all part of Tennis Australia's attempt to have the tournament happen despite a ban on international arrivals into the country.
Britain's Press Association news agency said Murray, apparently in good health, was hoping to arrive in Australia at a later date.
The 25-year-old American's announcement came just hours after former world number one and three-time major winner Andy Murray said he too had tested positive for the virus.
Murray, who has finished runner-up in Melbourne on five separate occasions, is currently isolating at home, and is still hopeful of competing in the tournament.
Australian Open 2021: Tennys Sandgren allowed to board charter flight despite positive COVID-19 result
Sandgren was given a special clearance to board one of the flights from Los Angeles to Melbourne despite testing positive to COVID-19 in November and again on Monday.
Thiem's father told Austrian media that he would train with Dominic and fellow Austrian Dennis Novak.
The Australian Open draw will be held on 4 February, four days ahead of the start of the main tournament, which ends 21 February with the men's singles final.
Australian Open 2021: Rafael Nadal's coach Carlos Moya to miss tournament due to COVID-19 travel restrictions
Nadal is aiming to clinch a 21st major title in Melbourne, which would put him ahead of Federer's 20 as the most successful men's player of all time.
Australian Open 2021: India's Ankita Raina loses to Olga Danilovic, eliminated in final round of qualifiers
In the women's singles qualifiers being held in Dubai, Ankita lost the third and final round 2-6, 6-3, 1-6 to her Serbian opponent in almost two hours.
Australian Open 2021: Denis Kudla tests positive for COVID-19, forced to pull out despite winning qualifier
The fourth seed learned of the positive test when 5-3 up in the second set against Moroccan Elliot Benchetrit, but was allowed to complete the ninth game.
"It really was just a situation where I didn't want to be away from my family for that long. So, I've decided to stay home," Isner said.
Australian Open 2021 qualifiers: Two players test positive for COVID-19, withdraw from qualifying tournament
Australian Open organizers said all players who started in the qualifying tournament had returned at least one negative test after arriving into Doha, where they were tested on arrival and isolated until they returned a negative result.
Organisers have branded the WTA 500 and ATP 250 events as the Melbourne Summer Series and named each tournament after areas of Victoria state.
Nadal can break a tie with Roger Federer for the most Grand Slam singles titles for a man after matching him with No. 20 at the French Open in October; by March, Djokovic can surpass Federer's record for most weeks at No. 1 in the ATP rankings