The depot reportedly contained tens of thousands of artillery shells.
Witnesses posted videos of balls of flame and black smoke, starting during the day and continuing after dark.
A state of emergency was declared in the area, west of the city of Krasnoyarsk.
Children at a nearby summer camp were taken to safety while soldiers at the base took refuge in bomb shelters.
About 3,000 people were moved, but Achinsk town officials told Tass news agency that 11,000 more residents were being prepared for evacuation.
The cause of the blast was not immediately clear.
Krasnoyarsk region is one of those affected by huge wildfires that engulfed parts of Siberia in recent weeks, due to unusually hot weather and strong winds.
The worst of the fires, however, were many miles away to the northeast.
The Achinsk ammunition store is one of the oldest in the Russian armed forces’ ordnance network and was due to be dismantled by 2022, Tass quoted the defence ministry as saying.