The singer said on his website he had hoped making music and performing would be enough to work through it but that he underestimated how hard his recovery would be.
The 49-year-old former Wham! front man was to perform in Sydney and other Australian cities in November and early December.
He still has concerts scheduled this month in the United Kingdom. They are makeup dates for shows he canceled after being hospitalized for pneumonia in Vienna in November.
Michael spent about three weeks in the hospital and said later that his health had been "touch and go."
He performed at the London Olympics closing ceremony in August.