In a statement published on the Telegram messaging app, Vyacheslav Gladkov said two industrial facilities in the border town of Shebekino had been shelled and four employees had been wounded.
Several settlements were left without electricity, he added.
Belgorod, which borders Ukraine's Kharkiv region, has repeatedly come under attack from Kyiv's forces since the beginning of the full-scale conflict in Ukraine in February 2022.
MNA/4452796; PR