A coastguard patrol boat found debris including part of the wing, seats and a liferaft just over 100 kilometres west of the island, a Jeju coastguard spokesman said.
Four coastguard boats and a helicopter are searching the area, he told AFP.
The Boeing 747-400 had taken off from Incheon at 3:05 am and was headed for Shanghai's Pudong airport.
The pilot called Jeju airport to request an emergency landing because of mechanical problems but the aircraft disappeared from radar screens soon afterwards, an Asiana spokesman said.
The transport ministry said in a statement the plane carrying a pilot and a co-pilot was believed to have caught fire in flight, but the circumstances could not be confirmed until the recovery of its flight data recorder.
The pilot radioed Chinese air traffic controllers in Shanghai that fire had broken out in the hold and that the plane had to divert to Jeju, a transport ministry official said.
"A Korean Air passenger flight picked up this message and alerted South Korean air control authorities," assistant director Park Joo-Hwan told AFP.
Yonhap news agency said the 58 tonnes of cargo contained unspecified inflammable material. The Asiana spokesman said he was unaware of the contents of the cargo.
Asiana is the country's second and smaller flag carrier. It largely operates short-haul routes into Asia.
Copyright AFP (Agence France-Presse), 2011