Thai police said that eight of the bombs went off in the capital of Yala province while seven exploded in the province's outlying districts on Thursday morning.
The army said that Muslim separatists had placed most bombs in or near banks to cause maximum civilian casualties as people collected their wages at the end of the month.
General Ongkorn Thongprasom, the senior army officer in the region, said: "We received some intelligence reports, but we did not anticipate it would happen inside banks, especially on the last day of the month. We don't believe they are that cruel."
Ongkom said that some of the bombs were planted by women and were carried in women's handbags or hidden in thick books carried by teenagers dressed in student uniforms.
An anonymous caller warned one bank it had been targeted, prompting a stampede to leave the building, just minutes before an explosion, police said.
Many of Thursday's bombs were set off by mobile telephones and at least one was defused before it could go off, police said.
The bombs were most likely set off by Thailand's Muslim separatists who began fighting the government in January 2004.
More than 1,500 people have been killed since then, mostly in the Muslim-majority provinces of Yala, Narathiwat and Pattani.
The Muslim activists are seeking to form an Islamic country separate from Thailand where the vast majority of people are Buddhist.