The former Wham! frontman said that he would complete his Symphonica Tour dates in Britain in October before seeking treatment.
He had been due to open in Australia in Perth on November 10 before performing in Adelaide, Sydney, Melbourne, Brisbane and Hunter Valley on December 1.
"I have ... announced the cancellation of the shows in Australia which breaks my heart," Michael said in a statement.
The 49-year-old "Careless Whisper" and "Faith" singer fell ill in Vienna last November and was treated under intensive care for a month for a life-threatening illness.
He was forced to postpone his tour but resumed it some 10 months later.
"Since last year's illness I have tried in vain to work my way through the trauma that the doctors who saved my life warned me I would experience," Michael said.
"They recommended complete rest ... but I'm afraid I believed (wrongly) that making music and getting out there to perform for the audiences that bring me such joy would be therapy enough in itself."
He said his return to the stage had brought him "great happiness" and that some of his recent performances were his best to date, but concluded:
"I was wrong to think I could work my way through the major anxiety that has plagued me since I left Austria last December.
"All that's left for me to do is apologize to my wonderful Australian fan base and to promise faithfully that as soon as I completed these shows here in the UK, I will receive the treatment which is so long overdue."
Tickets to his Australian concerts will be refunded.
Michael has sold an estimated 100 million records over his career, but he has hit headlines in recent years for his personal life more often than for his music.
In 1998 he was arrested in California for "engaging in a lewd act" in a public toilet and has had a string of run-ins with British police for possession of narcotics. He also served a term in jail for driving under the influence of cannabis.
(Reporting by Mike Collett-White)
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