The person was detained by airport police on suspicion of violating the aviation security law, a ministry statement said. The person’s identity and motive were not immediately released.
The law bars passengers from handling exit doors and other equipment on board, with possible penalties of up to 10 years in prison for offenders, the ministry said.
The plane with 194 people aboard was heading to the south-eastern city of Daegu from the southern island of Jeju.
The flight normally takes about an hour, and the incident occurred when the plane was approaching the Daegu airport at an altitude of 700ft (213 metres).
A video apparently taken by a person on board that was posted on social media shows some passengers’ hair being whipped by the air blowing into the cabin through the open door.
The passengers included teenage athletes on their way to a track and field competition. Some screamed and cried in panic, Yonhap news agency reported, citing their coach.
Yonhap quoted other passengers as saying they suffered severe ear pain after the door opened. It said some cabin crew shouted for help from passengers to prevent the door from being opened.
Twelve people were taken to hospitals for treatment.
Emergency officials in Daegu said the injured people suffered breathing problems and other minor symptoms.