Among those hurt was the bookie's administrator, RIA Novosti reported.
The attacker, who was not identified, tossed the grenade at security guards about 2 a.m. local time when they wouldn't let him in the office, police said.
The attacker was reportedly drunk.
Three of the victims were hospitalized in serious condition. A fourth person was treated at the scene for minor injuries.
Notable deaths of 2014 [PHOTOS]