Russia carried out an air strike on downtown Kramatorsk on the afternoon of 7 July, the city council has said.
According to the Donetsk regional military administration, at least one person was killed and six wounded.
Six buildings, including a multistoried apartment block, were damaged in what the administration described as a "conscious attack on civilians".
Local governor Pavlo Kiriyenko urged local residents to evacuation, saying "evacuation is a temporary measure while we must save lives right now!".
In April, Russia carried out one of its bloodiest attacks on Ukrainian towns when Kramatorsk was hit by a rocket strike which killed 57 civilians who gathered at the railway station, waiting to get evacuated.