The attacks were carried out at 10 a.m. local time with so-called glide bombs, according to Sloviansk Mayor Vadym Lyach. He said a seven-year-old girl was among the injured.
A video published by Ukrainian police shows the ruins of a completely destroyed house.
Sloviansk is located in the Donetsk region, which Russia claims to fully control. Russian forces are located about 15 kilometers from the city.
Russian state media is reporting that a priest has been killed in a Ukrainian attack on a village in territory occupied by Russia in the Zaporizhzhia region. According to authorities in the Russian city of Belgorod, another man has been killed in a Ukrainian attack on a border town in the region.
