The man, also suspected of involvement in a second blast a day later in Bangkok, was arrested at an apartment in a suburb of Bangkok, police spokesman Lt. Gen. Prawut Thavornsiri said.
However, he is not the man in a yellow T-shirt and dark-framed glasses who was identified from surveillance video as the chief suspect in the bombing, Prawut said.
"The man we have is not the man in the sketch, but we believe he is part of the network which carried out the two bomb incidents," he said.
Prawut initially said the suspect arrested Saturday was a Turkish national. But he subsequently told CNN: "At first we thought he is Turkish. But we just found out two Turkish passports he is holding are all fake.
"We also found many empty fake passports, also various kinds of evidences."
Prawut said investigators hunting for clues had "also found the same type of ball bearings in this man's apartment."
High ranking police officers, forensic experts and army personnel were all seen outside the building shortly after news of the arrest broke.
The apartment is in the Nong Jok suburb, an area known to house a large Muslim community.
The deadly explosion at Bangkok's Erawan Shrine -- a spot popular with tourists and locals -- wreaked havoc on August 17. The second blast, which occurred at a pier on the Chao Phraya River that flows through Bangkok, did not cause any casualties.
No claim of responsibility
Authorities have narrowed the description of the main suspect in the first blast to an unidentified foreigner who was caught on surveillance video hiding a backpack under a bench at the shrine
minutes before the bomb detonated.
The video footage showed a man in a yellow T-shirt and dark-framed glasses.
At least 10 people may have taken part in the bombing, but the attack is unlikely to be linked to international terrorist groups, Thai authorities said.
Police said a week ago that they no longer believed that three other people seen near the main suspect on surveillance video were involved in the attack
There has been no claim of responsibility for the bombing. Thai authorities haven't said what they think the motive for it might have been, other than making vague references to unspecified people or groups who want to hurt Thailand's tourism industry and economy.
Thai security forces are sharing information with Interpol, the global police organization, and with intelligence agencies from allied countries, officials said.
Royal Thai Police Commissioner Gen. Somyot Poompanmoung said last week that he believes "several teams" were involved in the preparation and execution of the attack, which killed at least 20 people and wounded more than 120.
"This operation was carried out by a big network," he said.
Police offered a reward for information leading to the suspect's arrest, but it's not clear if this was a factor in Saturday's operation.
Foreign visitors among blast victims
Bangkok, which was convulsed by political unrest last year, has experienced small-scale bomb and grenade attacks in the past but nothing of the magnitude of the shrine blast. Two devices exploded at an upscale shopping mall
in February but didn't cause any casualties.
The shrine is a major draw situated at a bustling intersection near a large shopping mall.
At least seven people from other Asian countries were reported to be among the dead as well as one Briton. The site is popular among Buddhists as well as Hindu and Sikh members of Thailand's Indian community.