If found guilty, Sergeant Stepan Khodorov could face up to 10 years in prison.
The commander of the unit also faces disciplinary action, for failing to report the incident.
The charge against Khodorov was revealed days after a brutal hazing incident in a military school in the city of Chelyabinsk caused public outrage in Russia.
That incident left one 19-year-old conscript maimed for life. Twelve serviceman have been charged over that attack. Protesters have called for the resignation of Defense Minister Sergei Ivanov over the Chelyabinsk incident.