A statement released by Malaysian police chief Ismail Omar late Wednesday said authorities arrested the suspect in the capital Kuala Lumpur at 3:30 pm (0730 GMT).
"The Iranian was arrested under the Immigration Act of Malaysia out of intelligence provided by Thai counterparts," the statement said.
"He is being investigated for terrorism activities in relation to bombings in Thailand."
The statement gave no further details, such as the suspect's name.
Malaysian police spokesman Ramli Yoosuf told AFP that Thai authorities had been informed of the arrest but he was as yet unaware of any Thai request for the suspect's extradition.
"I don't know how long the investigations will take," he said.
Tensions between Middle East arch-foes Iran and Israel have risen sharply following three bomb incidents in world capitals in less than 24 hours, but Iran has angrily rejected accusations that it was to blame.
On Monday, bombers targeted Israeli embassy staff in India and Georgia before escaping.
In Bangkok, two Iranians were detained over three blasts that occurred Tuesday. They were charged with causing an illegal explosion and other offences, Thai Foreign Minister Surapong Tovichakchaikul said.
"We cannot say yet if it's a terrorist act," he told reporters, "but it's similar to the assassination attempt against a diplomat in India."
One of the men -- named as 28-year-old Saeid Morati -- had his legs blown off as he hurled an explosive device at Thai police while fleeing an earlier, apparently unintended, blast at a house in the Thai capital, officials said.
He was unconscious but in a stable condition, according to the Bangkok hospital where he was treated.
A second Iranian suspect was detained trying to board a flight out of the country while the third had fled to Malaysia, they said.