The blasts near the town of Arys were caused by "a fire, which led to the explosion of some of the ammunition (at the depot)," Kazakhstan's defense ministry said in a statement.
Social media users shared videos of people fleeing the area with huge plumes of smoke rising towards the sky in the backdrop.
Health authorities said 46 people, including five children, were injured by explosions. Radio Free Europe's Kazakh service reported over 50 hospitalized, citing sources at two hospitals in the south of the country.
Three people in a hospital in Shymkent, a city of one million, were in a serious condition, RFE reported.
The head of the administrative region where Arys is located said that the town would be evacuated "completely" on Monday.
"Given the scale of what is happening, we see that we need to evacuate the city as a whole," Umirzak Shukeyev, Turkestan regional head, said in comments published by the private Tengrinews website.
The government has introduced a state of emergency and begun evacuating Arys' 45,000 residents. About 1,000 police and army troops have been sent to the area to maintain order.
Authorities also halted railway traffic in the area.
The explosions at the depot have been powerful enough to have been registered by the nation's seismic service.
The cause of the fire wasn't immediately clear. A criminal probe has been launched.
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