The explosion occurred on Thursday night when a fire broke out in the ammunition depot belonging to the Ministry of Defense.
A video from the incident shows how a plume of smoke rises from the fire, and then a powerful detonation.
The disaster authority states that more than 500 tonnes of dynamite were in the warehouse, and that debris from the explosion was found up to two kilometers from the site.
At a hasty cabinet meeting on Friday, President Kasym-Zhomart Tokayev said the country had "systematic problems" with its ammunition depots.
Several similar explosions have occurred in ammunition depots in Kazakhstan in recent years, including three in a facility near the city of Arys.