The attacker parked the bike rigged with explosives nearby and bought goods at the market to blend in with the crowd, police Lt. Eakapong Rattanachai said.
The bomb exploded when the attacker left the market area, causing the casualties, Eakapong said.
The explosion happened in Yala province, one of Thailand's three southernmost provinces where Muslim militants have waged a yearslong insurgency.
The three provinces are the only ones with Muslim majorities in the predominantly Buddhist country.
More than 6,500 people have been killed in the violence since 2004.
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