During a firearms training session, two men opened fire on a group who had volunteered to fight in Ukraine, state-owned news agency Ria reported.
The attackers were from a former Soviet republic, the Russian defence ministry said, but did not give further details.
They were also shot dead during the incident in the Belgorod region of Russia, which borders Ukraine.
A further 15 people were wounded.
“During a firearms training session with individuals who voluntarily expressed a desire to participate in the special military operation [against Ukraine], the terrorists opened fire with small arms on the personnel of the unit,” Ria cited a defence ministry statement as saying.
“As a result of the shooting, 11 people were fatally wounded. Another 15 people with wounds of varying severity were taken to a medical facility,” it said.
Last month Russian President Vladimir Putin ordered a mobilisation of 300,000 Russians who had previously done compulsory military service.
The order sparked protests across Russia, and a surge of people attempting to leave the country.
Defence minister Sergei Shoigu announced in early October that more than 200,000 reservists had already been drafted.