The first small explosions were heard during rush hour, just before 9 a.m. (0200 GMT) at two sites near central Bangkok. A third blast was heard shortly afterwards at a government complex hosting several ministries on the northern side of the city.
Four people were wounded, the Erawan Medical Center said. It added that "none are serious and all are receiving medical attention at hospitals."
Three of those hurt were women cleaning the street when a bomb went off. Pictures on local websites showed them looking dazed and getting treament from medics. One was seen being loaded into an ambulance.
The other casualty was from a device that exploded near the 77-storey King Power Mahanakhon building, one of the tallest in the city. Police Colonel Kamtorn Uicharoen told Reuters a total of six bombs exploded. One was recovered before it blew up.
There was no immediate claim of responsibility.
"I would like to condemn those causing the situation which destroys peace and damages the country's image," Thai Prime Minister Prayuth Chan-ocha said on Twitter.
"I have instructed officials to take care of public safety and those affected promptly."
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Bangkok is currently hosting a regional security meeting of foreign ministers from the Association of Southeast Asian Nations (ASEAN) and their counterparts from world powers including the United States, China and Russia.
None of the Friday blasts were very close to the meeting venue.
On Thursday, Thai police said they had found two fake bombs near the venue of the regional meeting. The packages prompted a brief security scare but were quickly deemed harmless. It was unclear whether the meeting was the target.
Police said two men had been arrested in connection with the fake bombs.
China's top diplomat Wang Yi and U.S. Secretary of State Mike Pompeo are attending the forum along with other regional and global officials.
Bangkok was last hit by a series of small bomb blasts in 2017. One man was jailed for planting a bomb that wounded 21 people at a hospital. He was an opponent of the then-military junta, which was led by current prime minister Prayuth.