The 23-year-old Welshman, a team pursuit gold medallist at the Rio Olympics, was slated to ride in the Tour Down Under this week.
Doull reported sick after the team's presentation and did not start the People's Choice Classic but that was clearly just a precursor to a more serious ailment.
Team Sky doctor Neil Heron said: "Initially Owain had a stomach bug and he had those symptoms for around 36 hours.
"He was starting to improve, but on Tuesday morning his stomach pain became a lot worse.
"We began to suspect appendicitis and he was taken to Royal Adelaide Hospital where they confirmed the suspected diagnosis.
"The earliest he will leave the hospital is Thursday and recovery and recuperation is likely to take at least four weeks.
"Owain is obviously disappointed, but he appreciates he needs to be 100 per cent fit to get back racing."