Vyacheslav Gladkov, writing on the Telegram messaging app, said the targets were downed as they approached the city.
Two people were being treated in hospital for injuries. Gladkov said windows were blown out in a multi-storey apartment building and at least 30 cars sustained damage.
Ukraine launched missile and drone attacks on Wednesday on Belgorod region, local officials said. Russia said 25 civilians, including five children, were killed in attacks last weekend.
(Reporting by Reuters; Editing by Sandra Maler)
