The explosion in the province of Pattani caused a fire that destroyed the store and injured a passerby.
Police told the Bangkok Post the bomb was one of a series of small bombs allegedly planted around the Muang district of Pattani by insurgents. Only two of them actually exploded.
Insurgents were also suspected in a series of arsons last week in the Yarang district of Pattani.
Investigators say the insurgents were trying to re-establish their credibility as a threat following an unsuccessful raid on a Thai marine base Wednesday in Narathiwat province that left 16 militants dead, the Post said.