Kyiv did not say where the strike took place, but stressed the soldiers were not taking part in a "mass gathering" and most were in their shelters during the attack.
The Ukrainian army has in recent weeks faced pressure to investigate what some see as glaring lapses in ensuring the safety of training soldiers.
Six soldiers training close to the border were killed by a Russian strike last month, in what one Ukrainian opposition politician called a "crime" by army leadership.
"Today, on June 1, the enemy launched a missile strike on the location of one of the training units of the Ukrainian army," the Ukrainian army said in a statement.
"As of 12:50 pm (0950 GMT), 12 people are known to have been killed and more than 60 wounded."
"If it is established that the deaths and injuries of the servicemen were caused by the actions or inaction of officials, those responsible will be brought to strict accountability," it added.
Separately on Sunday, the Russian army said it had captured another village in Ukraine's northern Sumy region, where Kyiv fears Moscow could mount a fresh ground assault.
Russia claims to have captured several settlements in the region in recent weeks, and has massed more than 50,000 soldiers on the other side of the border, according to Ukrainian President Volodymyr Zelensky.
Authorities in the region have evacuated more than 200 villages amid intensified shelling.
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