The Erawan Shrine, which was crowded at the time, is a major tourist attraction and foreigners, including Chinese, are among the casualties.
No-one has yet said they carried out the attack.
Defence Minister Prawit Wongsuwon said the bombers had “targeted foreigners… to damage tourism and the economy”.
“We will hunt them down,” he said.
Bangkok blast: The events of the day
Images from the scene
The Nation TV channel quoted Prime Minister Prayuth Chan-ocha as saying the government would set up a “war room” to co-ordinate its response.
National police chief Somyot Poompummuang said that 10 Thais had been confirmed dead, along with one Chinese and one Filipino.