Ten wounded people, including a 13-year-old, were taken to hospital with minor injuries, Khinshtein wrote on Telegram.
“What happened today is a huge tragedy for all of us,” he said. “We grieve together with the families of the victims. No one will be left without support.”
Those responsible would receive “well-deserved retribution”, he said.
Russia’s permanent representative to the United Nations, Vasily Nebenzya, later told a session of the Security Council that Moscow would be quick to respond to the “unambiguous move by the Kyiv regime”.
“As you can well understand, our response to this targeted crime against peaceful Russian citizens will not be long in coming,” he told the session.
Ukrainian authorities have not commented on the incident.
Khinshtein said Ukraine had fired U.S.-supplied HIMARS rockets, damaging several buildings including a school, recreation center, and private residences in Rylsk, some 16 miles (26 km) from the border with Ukraine’s Sumy region.
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