The attack took place around noon Narathiwatone of the southernmost provinces in the country.
Low-level conflict has simmered in Thailand south since 2004, killing more than 7,000 people as rebels in the Muslim-majority region fight for more autonomy from the state.
Governor of Narathiwat Sanan Pongaksorn told AFP that a suspect drove a car into the police compound before abandoning the vehicle.
Shortly after the car was parked, a bomb exploded, the governor said, adding that police were reviewing security camera footage to identify the suspect and investigate possible motives.
He said one person was killed and 28 others were injured, two of them in critical condition.
The southern region—heavily guarded by Thai security forces—differs culturally from the Buddhist-majority Thailand that colonized the border region with Malaysia more than a century ago.
In September, a roadside bomb killed a police officer and wounded three others.