The blasts occurred at a military base near Kalynivka in the Vynnytsya region, 270km west of Kiev, Ukrainian emergencies service said in a statement.
One person was injured, it said.
The area was also closed to rail and road traffic. The national railway company Ukrzaliaznytsya diverted 14 passenger trains.
Arriving in the region hours later, Prime Minister Volodymyr Groysman said "external factors" were behind the incident.
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The depot houses some 188,000 tonnes of munitions, including projectiles for various rocket-launch systems.
The fire tore through a major munitions, setting off artillery shells, forcing the closure of airspace for 50 kilometres around and the evacuation of residents, officials and reports said.
The fire broke out at about 10pm (2000 GMT) the Ukrainian army high command said on Facebook.
It was the second major incident affecting a Ukrainian weapons depot this year. And while the cause was not immediately clear, military authorities were investigating the possibility of sabotage or negligence.
It was not immediately clear how extensive the damage from the explosions was, but local media described the depot as one of the largest in the country.
Local authorities said they had ordered the evacuation of Kalynivka and two neighbouring villages, while urging people not to panic.
"Airspace has been closed in a radius of 50 kilometres (30 miles) around the area of the fire," deputy infrastructure minister Yuriy Lavrenyuk said on Facebook.
Prime Minister Volodymyr Groysman arrived at the site shortly after midnight to coordinate the emergency response, his office said.
The city of Vinnytsia, the administrative centre of the region, was not in danger, its mayor said.
