Gladkov, writing on the Telegram messaging app, said the attacks broke windows and caused other damage to several sites in the town, including two schools and four educational institutions.
There was also damage to property in areas outside the town.
Pictures posted on social media showed a car bursting into flames and a fire in a courtyard.
Ukraine has in recent weeks regularly launched air attacks on Belgorod, and two nearby Russian regions, Bryansk and Voronezh. There have also been land incursions in Belgorod.
(Reporting by Ron Popeski; Editing by Sandra Maler)
