A fifth soldier was seriously injured and was being treated in hospital, according to a statement by the defence ministry published by the Hungarian news agency MTI.
The incident took place in the Hortobagy National Park close to the city of Debrecen, 230 kilometres (140 miles) east of Budapest, used by the military.
The remote and sparsely populated area was used as a shooting range by the Hungarian Army for decades following World War II.
Since 2013, military explosives experts have been working to clear the area of unexploded devices.
Army Chief of Staff Tibor Benko told MTI that the cause of the explosion was as yet unclear and that an immediate investigation has been ordered.
