More than 20 people were killed and scores injured in an explosion at the Hindu shrine which is also popular with Thai Buddhists on Monday evening.
Thai police say the main suspect is a young man seen entering the shrine with a backpack then leaving without it, reported BBC.
Prime Minister Prayuth Chan-ocha has said the incident was the worst ever attack on Thailand.
A second explosion rocked Bangkok on Tuesday which caused panic but no injuries or damage were reported. Authorities have not ruled out a link between the incidents.
The explosive device was thrown from the Sathorn bridge near a parking lot, bounced into the water and exploded there.
Sathorn pier is a major terminal linking Chao Phraya River commuter boats and the nearby Skytrain station. It's also a major touriststop, especially for Chinese tour groups.
National police spokesperson Prawut Thawornsiri said on Wednesday that police were also looking for accomplices of the main suspect.