Police say the explosive devices were designed to cause panic, rather than death, but it's not known why they were planted and no one has claimed responsibility.
Thailand's military overthrew the Southeast Asian nation's elected government in May, and analysts say the army is likely to use Sunday's blasts as a reason to prolong martial law.
The explosions came a little more than a week after the junta-appointed legislature formally impeached former Prime Minister Yingluck Shinawatra, the leader of the ousted government, for her role in overseeing a government rice subsidy program that lost billions of dollars.