The suspect, named as 57-year-old Norouzi Shaya Ali Akbar, faces charges of possessing and making explosives, said deputy national police chief Pansiri Prapawat.
He was filmed by a closed-circuit television camera leaving a house rented by the bomb suspects shortly before a string of blasts on February 14, and is believed to have fled to Iran the same day, he said.
"Thai authorities will seek him through diplomatic channels," Pansiri added.
Police said they were also gathering information on a potential sixth suspect.
On Friday Thai police had said they were hunting for another Iranian named as Nikkhahfard Javad. It was unclear Monday whether he was still a suspect in the case and no arrest warrant has been issued.
The kingdom has stepped up security following Tuesday's blasts, which was the third bomb incident to shake world capitals in less than 24 hours.
Thai police have said that Israeli diplomats were the intended target of the plot, but Tehran has rejected accusations that it is behind a terror campaign against the Jewish state.
Arrest warrants have been issued for four other Iranians, two of whom have been detained and charged over the botched attack, which came to light after an apparently unintended explosion at a Bangkok house.
One of them -- named as 28-year-old Saeid Moradi -- had his legs blown off as he hurled a bomb at Thai police while fleeing. Another, Mohamad Khazaei, was detained trying to board a flight out of the country.
Thailand is seeking the extradition of another Iranian arrested in Malaysia in connection with the blasts, while an Iranian woman who rented the house used by the suspects in Bangkok is thought to have fled the kingdom.
In handcuffs and a bullet proof vest, Khazaei was taken by police on Monday to the scene of the first blast as part of the investigation.