Dnipropetrovsk region Governor Sergiy Lysak described the air assault as "large-scale" and said a young girl and an elderly woman were among the dead.
The attack targeted residential and office buildings in Kharkiv, causing several blazes, Ukraine's state emergency service said.
Over 20 Russian drones struck Dnipro, damaging a hotel, homes, service stations, and a restaurant complex.
Russia’s military said its air defense systems shot down 19 Ukrainian drones across the country and annexed Crimea overnight.
Regional authorities urged residents to avoid areas near the border with Ukraine that regularly come under attack.
Among the dead were three couples — men and women between the ages of 61 and 74 — Ukrainian prosecutors said.