At least 35 people died in the strike on the Yavoriv training base, near a major crossing point into Poland used by refugees from the conflict.
Russia fired around 30 cruise missiles at the facility, outside the city of Lviv, early on Sunday, the local governor told the BBC.
Most were intercepted, though, he said.
But several hours after the attack, ambulances were still rushing to the scene, and the authorities were conducting search-and-rescue operations.
Video of the aftermath of the attack posted online and verified by the BBC showed a huge crater at the site and a massive fire at a small building nearby.
Dukhnych Vitalii, a 19-year-old student who lives in a nearby apartment complex, said “the night sky turned red” as the missile struck.
“We woke up when we heard the explosion,” he said. “It looked scary.”
His 25-year-old cousin was training at the centre, the teenager said, and his family had yet not managed to contact him.
The base, also known as the International Peacekeeping and Security Center, has previously been used for military training of Ukrainian troops, often with instructors from the US and other Nato countries. It was not immediately clear whether foreign instructions were at the centre when it was hit.
This attack is significant because the centre, one of Ukraine’s largest military facilities, is located just 25km (15 miles) from Poland, a Nato member.
The border with Poland is a vital route for refugees, but also for weapons being sent by countries in the military alliance – which have included anti-tank and anti-aircraft missiles.
So far, Nato has rejected a Ukrainian request to establish a no-fly zone over Ukraine, saying this would trigger a wider conflict with Russia.
It is also the first major attack in western Ukraine since Russia launched its invasion of the country, on 24 February. The region has become a hub for millions of people escaping the war in other areas of the country. Around 2.6 million have left Ukraine so far.
Hours earlier, Sergei Ryabkov, the Russian deputy foreign minister, said Moscow had warned the US that “pumping weapons from a number of countries it orchestrates isn’t just a dangerous move, it’s an action that makes those convoys legitimate targets”.
Speaking to the BBC, the mayor of Lviv, Andriy Sadovyy, said it was necessary to “close the sky” to prevent Russia from carrying out aerial strikes.
“Europeans, understand this situation: it’s easy to talk and drink coffee and say they’re deeply concerned… but every hour the skies are not closed, the Russians are killing civilians and children,” he said.
“We need closed sky. We need decision today. We need bullet-proof vests today, not tomorrow. Tomorrow Russian missiles [will] end up in the European Union.”
