The base belongs to Russia's National Guard, a branch established last year to defend borders and counter extremism.
It is subordinate directly to President Vladimir Putin and has bases in the country's volatile North Caucasus regions, including Chechnya.
In a statement, the National Guard said the rebels tried to storm the base in heavy fog at around 2:30 am local time (2330 GMT on Thursday) but were spotted by a group of soldiers who opened fire.
"Six of the attackers were destroyed," the statement said. "During the armed combat, six military were killed and there are wounded."
None of the insurgents managed to enter the base, the National Guard said.
Counter-terrorism troops, investigators and explosives experts are at the scene, it said.
The SITE Intelligence Group, which monitors jihadist communications, said the Islamic State group claimed responsibility for the attack on Friday.
The assailants attacked "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."
Chechnya was the scene of two separatist wars in the 1990s and early 2000s, but violence in the region has largely been suppressed under the iron-fisted rule of strongman leader Ramzan Kadyrov.
On Friday Kadyrov promised to wage a "ferocious fight" against the jihadists.
"These demons have treacherous intentions: as we have seen they do not want to stop," he said, according to the Interfax news agency.
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 were also killed.
The Russian North Caucasus is one of the major sources of foreign jihadists fighting in Syria and Iraq.
In January, Kadyrov said his forces had detained more than 50 insurgents linked to the Islamic State group in a security operation.
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