The shooter began what police described as "random fire" with a rifle in a street in the city of Belgorod before entering a nearby store, RIA Novosti reported.
Five of the victims were declared dead at the scene and the sixth a short time later at a hospital, officials said.
The assailant fled in a vehicle that was later found by police.
Special Forces officers were deployed to the home of a man suspected in the attack. Police described him as a man around 30 years old with a criminal record.
The attack follows an incident six months ago in Moscow in which an attorney killed six people after the end of a romantic relationship.