At least 11 apartment buildings and 39 private houses were damaged, while five homes were completely destroyed, said governor Vyacheslav Gladkov on Telegram.
Mr Gladkov had earlier said the city of nearly 400,000 was rocked by a series of blasts, adding: "Presumably, the air defence system worked."
At least four people were injured and two hospitalised, including a 10-year-old boy, he said.
The reports could not be independently verified. Ukraine has also not yet officially reacted to the incident.
Senior Russian politician Andrei Klishas accused Ukraine of the attack on Belgorod and sought a military response.
"The death of civilians and the destruction of civilian infrastructure in Belgorod are a direct act of aggression on the part of Ukraine and require the most severe - including a military - response," Mr Klishas wrote on Telegram.
This is, however, not the first time that Moscow has accused Kyiv of attacking a bordering region. While Ukraine has not claimed responsibility for the attacks, it described them as payback for their invasion.
The reported blasts come as an adviser to Ukrainian president Volodymyr Zelensky conceded on Sunday that Kyiv could lose control of a key bastion in the eastern province of Luhansk to Moscow.
And earlier on Saturday, Ukraine’s state emergency service probing the 27 June bombing of a shopping mall in Kremenchuk found up to 29 body fragments in the wreckage. The bombing had claimed 21 lives while 66 were injured.
Russian president Vladimir Putin had said that troops intended to hit a weapons depot nearby, denying that the mall was a target.
Thousands of civilians have been killed and cities levelled since Russia invaded in what Mr Putin described as a "special military operation" to demilitarise and "denazify" Ukraine.
Moscow is now focused on driving Ukrainian forces out of Donetsk and Luhansk, with its military closing in on the last-standing city of Lysychansk.
While a Ukrainian army spokesperson said that the city has not been seized by the Russian forces, pro-Moscow separatist leader Rodion Miroshnik told Russian television that “Lysychansk has been brought under control”, though he added it was “not yet liberated”.
Earlier, Oleksiy Arestovych, an adviser to the Ukrainian president admitted that the city may fall. “I do not rule out any one of a number of outcomes here,” he said. “Things will become much more clear within a day or two.”
Additional reporting from the wires
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