Images of the suspect caught on CCTV footage had already been released.
In the new footage, the suspect shown carefully and deliberately removing his backpack inside the shrine, getting up without it and immediately leaving the scene.
The spot where he was sitting is precisely where the bomb went off a few minutes later, says the BBC's Jonathan Head in Bangkok.
"There is a suspect... we are looking for this guy," Prime Minister Prayuth Chan-ocha told reporters.
"The yellow shirt guy is not just the suspect. He is the bomber," police spokesman Lt Gen Prawut Thavornsiri told the Associated Press news agency.
The bomb was detonated at about 19:00 local time (12:00 GMT) on Monday when the shrine, and the nearby Ratchaprasong junction, were crowded.
"There have been minor bombs or just noise, but this time they aim for innocent lives. They want to destroy our economy, our tourism."
In a televised address, he pledged the government would do all it could to bring the perpetrators to justice and told foreigners living in the country that it would try to safeguard them.
In Tuesday's incident, a device - possibly a grenade - was reportedly thrown at the busy Sathorn pier in Bangkok. (bbcasia)