The man opened a door of the aircraft minutes before it was due to land in the city of Daegu, officials said
The MiG was on an air patrol when it dropped off the radar in eastern Romania between the villages of Cogealac and Gura Dobrogei.
The pilot of the IAR 330-Puma helicopter sent to find him had reported unfavourable weather and had been called back to base before it too crashed, the ministry said.
Romania, a European Union and NATO member, plans to phase out its MiG planes and is flying F-16s.