Interior Minister Ihor Klymenko said bodies of the school’s director, deputy director, secretary and a librarian had been pulled from the rubble by rescue workers on Wednesday.
Klymenko added a number of local residents were injured as they had been passing the building at the time.
Photos shared by Klymenko on the Telegram messaging app showed emergency workers carrying away a body on a stretcher.
A photo released by police showed rescue workers standing in front of a devastated building and rubble.
The regional military administration said a drone fired by Russia had hit the school at 10.05am (7.05am GMT).
Ukrainian human rights ombudsman Dmytro Lubinets said on Telegram: “The school building was destroyed, and this is just before the school year, which unfortunately will never start for some.”
Russia denies deliberately targeting civilians and civilian infrastructure.
Meanwhile, three people have been killed in Russian President Vladimir Putin’s troops fired artillery near the eastern Ukrainian city of Lyman.
Authorities say two women and a man aged 63 to 88 were sitting on a bench in the village of Torske when shelling hit.
The area is close to the front line and regularly comes under attack.
In addition, a drone attack on the Danube river port of Izmail destroyed 13,000 tons of grain.
Deputy Prime Minister Oleksandr Kubrakov said the grain had been destined for export to Egypt and Romania.
Over the past month Russian strikes on Ukraine’s sea and river ports had destroyed 270,000 tons of grain, he said.
Elsewhere, there have been reports of explosions in the port city of Sevastopol in Russian-occupied Crimea.