Okhtyrka was worst hit, where drones damaged or destroyed 13 homes and injured a family with three children.
The assault, carried out with Shahed-type drones between midnight and shortly after on Wednesday, triggered more than 20 explosions across the city, according to local reports.
A woman was rescued from the rubble of one destroyed structure.
Ukraine’s Air Force said Russia fired 93 drones and two Iskander missiles across the country, with 62 drones and one missile intercepted.