The attack took place in the early hours of Sunday and left the school all but unusable.
A police spokesman said there had been no one in the building at the time.
After capturing the Luhansk region earlier this month, Moscow continues to turn its attention to the Donetsk region, which is only partly under the control of Russian separatists.
Although no large-scale offensive has yet been launched, sporadic fighting and shelling have been underway in various areas.
Russia’s Ministry of defence released video footage of more of its military hardware being deployed in Ukraine.
Meanwhile in the northeast region of Kharkiv, the mayor of Chihuiv said her town was hit by 12 rockets in the early hours of Monday morning.
Galina Minayev was unclear if anyone had been killed but she said she feared people would be found under the rubble.
“All these years our society, residents have been creating, and building comfortable life conditions,” said Minayev, surveying the damage, “and now the enemy is destroying all this, killing children, peaceful residents. It’s very hard to describe all this.”
Kharkiv, Ukraine’s second-largest city, is thought to be one of the next targets of Vladimir Putin although Ukraine’s military, which is patrolling its outskirts, doubts Moscow has the troop numbers in the area to take it.
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