Regional governor Vyacheslav Gladkov said a residential area had been hit, and in a Telegram posting urged all residents to move to air raid shelters as sirens sounded around the city.
The Belgorod region, which adjoins northern Ukraine, has like other Russian border zones suffered shelling and drone attacks all year that authorities have blamed on Ukraine.
Images posted by the state-run RIA news agency showed at least three cars on fire, and other images posted online showed black smoke rising from the city.
Two residents told Reuters they had seen air defence missiles rising into the sky followed by explosions in the air and then louder blasts.
The Kommersant newspaper cited a source close to the Russian Investigative Committee as saying missiles fired from a multiple rocket launcher in Ukraine's Kharkov region had hit a skating rink on the central Cathedral Square, a shopping centre, residential buildings and a car.
No official comment was immediately available from Kyiv, which rarely claims responsibility for attacks inside its neighbour.
But the Ukrainian news outlet RBC-Ukraine quoted sources as saying Ukrainian forces had struck military targets in Belgorod in response to Russian bombardment of Ukrainian cities the previous day.
Russia, which invaded Ukraine in February 2022 in what it calls a "special military operation", unleashed its biggest air attack of the war on Friday.
Ukrainian officials said 31 civilians had been killed and more than 160 wounded in strikes on cities and infrastructure across Ukraine.
Alexander Bogomaz, governor of the Bryansk region which also adjoins Ukraine, said on Saturday a child had been killed in strikes on "civilian objects" in two villages, without specifying when the attacks took place.
The previous day, Russia's Defence Ministry said its anti-aircraft units had destroyed 13 Ukrainian rockets over the Belgorod region, and Gladkov said one person had been killed and four injured.
(Reporting by Maxim Rodionov; Editing by Kevin Liffey and Jan Harvey)
