A statement says the 48-year-old former Wham! frontman "is responding to treatment and slowly improving."
The statement issued Friday says Michael "is ill with pneumonia and any other speculation regarding his illness is unfounded and untrue."
Michael was hospitalized in Vienna earlier this week, and canceled shows in Vienna, Strasbourg, France, and Cardiff, Wales.
The Austrian doctors treating Michael say he has "severe community acquired pneumonia" but "his condition has stabilized and he is responding to treatment."
The singer has canceled dates in Liverpool, Sheffield, Newcastle, Glasgow, Birmingham, Manchester and London.