The blast late on Wednesday evening was thought to have happened when soldiers were moving hand grenades at the store in the western province of Afyon.
Environment Minister Veysel Eroglu said the explosion was most likely caused by an accident and he ruled out terrorism.
It is thought many of the soldiers were trapped inside the building as firefighters tackled the huge blaze.
Rescuers found it difficult to reach the soldiers because hand grenades lay strewn around the area, reports said.
Identification of those killed at the scene was impossible because of the force of the explosion, Hurriyet newspaper said.
A large fire burnt at the complex for several hours and emergency services had difficulty responding to the incident because of the high security in place.
The wounded have been sent to a military hospital for treatment.