All 169 passengers and seven crew members were able to leave the plane, with three having minor injuries, fire officials in Busan said.
The fire service was alerted to the fire which began inside the plane just before 10.30pm, it said.
South Korea's Yonhap news agency said it began in the plane's tail.
Footage aired by local broadcaster YTN shows evacuation slides deployed on both sides of the single-aisle plane, with emergency workers tackling smoke and flames from the jet.
Officials say all 169 passengers and seven crew members were able to leave the plane. (AP PHOTO)
Later footage from Yonhap news showed burned out holes along the length of the fuselage roof.
It is a month since the deadliest air disaster on South Korean soil when a Jeju Air plane coming from Bangkok crashed on Muan Airport's runway as it made an emergency belly landing, killing all but two of the 181 people and crew members on board.
Budget airline Air Busan is part of South Korea's Asiana Airlines, which in December was acquired by Korean Air.
Plane maker Airbus said it was aware of reports about the incident and was liaising with Air Busan.
Air Busan and Asiana did not immediately respond to requests for comment.
Korean Air directed inquiries to Air Busan.
The plane is a 17-year-old Airbus A321ceo model with tail number HL7763, according to Aviation Safety Network, a respected database run by the Flight Safety Foundation.
