The blast happened at a military base where hand grenades are stored.
Forestry and Water Minister Veysel Eroglu ruled out a terrorist attack and said the cause was accidental.
It is thought many of the dead were trapped inside the building as firefighters tackled the blaze.
Such was the power of the explosion residents in the provincial capital, Afyonkarahisar, took to the streets thinking an earthquake had struck.
It is believed the blast happened as soldiers moved hand grenades at the store.
There are reports that rescuers found it difficult to reach the soldiers because hand grenades lay strewn around the area.
One newspaper reported identification of those killed at the scene was impossible because of the force of the explosion.