The blast happened on Wednesday night at a military storage for hand grenades in the western province of Afyon.
Environment Minister Veysel Eroglu said the explosion was most likely caused by an accident and he ruled out a terrorist attack.
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 burned 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.
On hearing the blast, witnesses described residents in the provincial capital, Afyonkarahisar, taking to the streets believing an earthquake had struck.
“It was probably caused after a hand grenade was dropped,” Veysel Eroglu told reporters.
The soldiers’ deaths come at a time of heightened activity by the Turkish military.
Turkish warplanes have reportedly carried out strikes against Kurdish position in the south-east near the border with the Syria.
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