The explosion occurred in the Bakirkoy district in the European part of the city at 3:30 p.m. local time (12:30 p.m. GMT). One of the injured is in serious condition after sustaining head injuries, Kanal 7 television reported.
Police said a stun grenade that produces a lot of noise had been detonated near the store. It also shattered windows in several nearby shops.
The explosion came amid growing tensions in Turkey over attacks by separatist Kurdish radicals. But none of the organizations has so far claimed responsibility for the explosion. Police say Kurdistan Workers' Party could be behind the attack.
In late May, a suicide bomb attack in Ankara killed eight people and injured 100. Turkish officials blamed the party. The group denied involvement.