"Three people, including a small child, died," Gladkov said on Telegram.
The governor said two injured people are in intensive care.
Earlier, he said two people were killed when debris from the drone, shot down by Russian air defenses, fell near Belgorod and caused a fire in a house, adding that a child could be under the rubble.
Ukraine has been sending drones into the Russian territory almost daily since it launched a counteroffensive in early June. The United Nations said in August, following a botched drone strike on Moscow, that it did not want to see any targeting of civilian infrastructure.