The attack on Belgorod, which lies near the border with Ukraine, took place on Tuesday, according to Russia's ministry of defence.
One man was killed by a rocket that landed next to his car and four people were injured at an auto market, regional governor Vyacheslav Gladkov said.
A number of houses and cars were also damaged, according to officials in Moscow.
In all, Russian air defence claimed to have taken down 17 Ukrainian "air targets" aiming at Belgorod, including missiles fired from multiple rocket launchers, the Reuters news agency reported.
Russia says its attacks on Ukraine target only "military installations," while describing strikes on its territory as "terrorist attacks," Poland's state broadcaster Belsat noted.
Earlier on Tuesday, Russian missile and drone strikes on the Ukrainian
capital Kyiv and the northeastern city of Kharkiv killed at least five people, injuring dozens and creating substantial damage, according to news outlets.
The Kremlin leader Vladimir Putin on Monday said Russia would "intensify" strikes on Ukraine following Saturday's Ukrainian air attack on Belgorod, which Moscow said killed 25 civilians.
On Friday, Russia launched the largest attack of the war, killing at least 39 Ukrainian civilians, the Reuters news agency reported.
More Russian air assaults on Ukraine followed on Sunday and on New Year's Day, according to news outlets.
Tuesday is day 678 of Russia’s war on Ukraine.
Russia invaded Ukraine on February 24, 2022, launching the largest military campaign in Europe since World War II.
(pm)
Source: Reuters, Belsat, The Moscow Times
