The attack on Kostiantynivka came just hours after a deadly drone attack near Kyiv, where two people were killed and two others injured in a drone attack late on Tuesday evening, according to the Prosecutor General on Telegram.
One of the dead in Kyiv is said to have been a journalist, according to her employer Ukrinform.
According to the Ukrainian air force, Russia fired 177 drones of various types at targets across the country during the night.
In the metropolis of Kharkiv, two people were injured when a Russian drone crashed into a nine-story residential building, also late on Tuesday evening, according to Ukrainian rescue services.
The attack on the apartment building followed several attacks on the city and region of the same name late on Tuesday, according to Kharkiv's mayor Ihor Terechov.