Rufin Rahimov died as a result of careless handling of a weapon, the Defence Ministry's deputy spokesman, Teymur Abdullayev, said.
Rahimov died at a military unit in Balajari, near Baku. He had been called up by the Kapaz military enlistment office.
An investigation is under way.
In a separate incident, a soldier died of carbon monoxide poisoning at a military unit in Guba. Amiraslan Rustamov died in the boiler room.