Six attackers stormed "a military base of the Russian National Guard close to Naurskaya village in northwestern Grozny in Chechnya," the IS statement said. "They clashed with those at the base with light weapons for several hours."
The statement said all of the assailants died during the attack, which killed six Russian soldiers.
Russia's National Guard, established last year, is a new branch of troops aimed at defending borders and countering extremism.
In a statement, the National Guard said the rebels tried to storm their base in heavy fog at around 2:30 AM local time but were spotted by a group of soldiers who opened fire.
Two National Guard soldiers were killed in a Chechen village in January during a joint operation with police and special forces in which four suspected militants also died.