Prawit Wongsuwan vowed to hunt down the perpetrators of the attack in the capital, which killed at least 21 people and injured more than 120.
The Erawan Shrine is a major tourist attraction and foreigners are among the casualties.
The attack has not been claimed and it is unclear who would target the site.
The bomb was detonated at about 19:00 local time (12:00 GMT) on Monday.