The fire engulfed the aircraft carrying 181 people when it skidded off the runway just after landing and struck a barrier.
The country’s emergency office said its landing gear appeared to have malfunctioned.
The National Fire Agency says that a total of 62 people on board have been found dead as a result of the incident.
That toll is expected to rise.
Footage of the crash aired by YTN television showed the Jeju Air plane skidding across the airstrip, apparently with its landing gear still closed, and colliding head-on with a concrete wall on the outskirts of the facility.
The transport ministry said the incident happened at 9.03am local time (11.03am AEDT).
The National Fire Agency said the fire was almost put out but officials were still trying to pull people from the passenger plane at the airport in the southern town of Muan.
Emergency workers pulled out two people — one passenger and one crew member.
It said it deployed 32 fire trucks and several helicopters to contain the fire.
Emergency officials said they were examining the cause of the fire.
Local TV stations aired footage showing thick pillows of black smoke billowing from the plane engulfed with flame.
The incident came as South Korea is embroiled in a huge political crisis triggered by President Yoon Suk Yeol’s stunning imposition of martial law and ensuing impeachment.
Last Friday, South Korean lawmakers impeached acting President Han Duck-soo and suspended his duties, leading Deputy Prime Minister Choi Sang-mok to take over.
Choi ordered officials to employ all available resources to rescue the passengers and crew, according to Yonhap news agency.
Yoon’s office said his chief secretary, Chung Jin-suk, will preside over an emergency meeting between senior presidential staff later on Sunday to discuss the crash.
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