The national anti-terror committee said the attacks occurred on a busy street in the centre of the Dagestan capital Makhachkala.
The assailants managed to flee the scene, it said.
According to the local branch of the Investigative Committee, the shops sold alcoholic drinks.
It appears possible the liquor shops were specifically targeted by Muslim extremists.
Dagestan is the frequent site of attacks blamed on Islamist rebels who have been waging an insurgency against the pro-Kremlin local authorities.