The pilot was the only person on board the freight flight from Devonport to King Island in Tasmania on 8 November.
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.
The Piper PA-31 aircraft, operated by Vortex Air, had been due to complete the 240km trip at 07:15 local time.
"During the cruise, the pilot fell asleep, resulting in the aircraft overflying King Island by 46 kilometres," the ATSB said in a brief statement.
Aviation expert Neil Hansford said that Australia had strict rules relating to pilot fatigue.
"There is no way in the world that someone should've taken on that flight fatigued," he told the Australian Broadcasting Corporation.
On its website, Vortex Air says it runs charter flights for "groups, corporates and leisure travellers" around Australia.
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.
More about: Australia