The incident occurred in the town of Klintsy, some 50 kilometres (miles) from the Ukrainian border.
“A few houses were damaged and four people injured, according to preliminary information,” regional governor Alexander Bogomaz wrote on the Telegram messaging app.
Reuters was unable to immediately verify the report.
Residents posted footage to social media of a Russian military helicopter hovering over the town after the shelling and reported that electricity and water had been cut off.
Officials in Russian regions bordering Ukraine have in the past few weeks reported cases of what they said was cross-border shelling that damaged residential buildings and injured some people.