STORY: The attack was the latest in a series of Russian strikes in recent weeks using long-range missiles on crowded buildings in cities far from the front, each killing dozens of people.
Russia, which denies targeting civilians, said the building it struck on Thursday was used to train troops.
Ukraine said it was an office building housing a cultural center used by retired veterans.
Oleksandr Kutovyi is a spokesman for the emergency ministry in the Vinnytsia region.
He said not everyone reacted to the the air raid sirens:
"There were people inside, they were rehearsing for a concert that was to take place in the evening. Apart from this, as far as I know, a singer Oleh Skripka was going to take part in a meeting there..."
Ukraine's state emergency service said three children, including a four-year-old girl, were killed in Thursday's attack.
Another 71 people were hospitalized and 29 people were missing.