The Australian star withdrew from the Sydney Tennis Classic hours before he was due to face Fabio Fognini.
The 26-year-old had already pulled out of the Melbourne Summer Set last week after struggling with an unknown illness that affected his asthma.
He was tested for coronavirus but all had come back negative until Monday.
With the first grand slam of 2022 just one week away, Kyrgios hopes he will recover in time to enter the draw.
“Hey everyone, I just want to be open and transparent with everyone, the reason I have had to pull out of Sydney is because I tested positive for Covid,” he wrote on Instagram.
“I am feeling healthy at the moment with no symptoms. I wish everyone all the best and to stay safe where you can.
“If all goes well I will see you all at the Australian Open.”
Kyrgios has not played a singles match since losing to Stefanos Tsitsipas at the Laver Cup last September and has dropped to 114 in the world rankings.
The former world number 13, who lost a thrilling five-set match with Dominic Thiem in the round of 32 in Melbourne last year, has only once gone as far as the quarter-finals at his home grand slam.
He reached the last eight in 2015, where he lost in straight sets to beaten finalist Andy Murray.
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