Several MPs and senior leaders were rounded up by police as they left the National Assembly building in the capital on Monday night
The pilot was the only person on board the Piper PA-31 aircraft from Devonport to King Island in Tasmania on November 8, the BBC reported.
The incident, classified as a case of "incapacitation", is being investigated by the Australian Transport Safety Bureau (ATSB).
Officials have not said how the pilot awoke before landing the plane safely.
"During the cruise, the pilot fell asleep, resulting in the aircraft overflying King Island by 46 kilometres," the ATSB said in a statement.
The ATSB said it would interview the pilot and review operating procedures before releasing a report next year.
Last year, five people died when a plane on its way to King Island crashed moments after takeoff in Melbourne.
Several MPs and senior leaders were rounded up by police as they left the National Assembly building in the capital on Monday night
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