Malaysian police chief Khalid Abu Bakar said they were detained a few days ago and were assisting with the investigation.
Thailand has launched a manhunt for those responsible for the bombing which killed 20 people and injured 120 on August 17.
Thai police have arrested two people and are searching for a third man, said to be from China’s Xinjiang region.
Khalid Abu Bakar told reporters on September 14 that the three suspects are a Pakistani man, a Malaysian man, and a Malaysian woman, who were arrested based on a tip-off from Thai authorities.
He said the suspects would not yet be transferred to Thailand, as Malaysian police are still investigating. He did not give further details on the reason for their detention.
No group has stepped forward to claim responsibility for the attack at the Erawan shrine, but Thailand has alleged that a network which includes foreigners was behind the bombing.
Over the weekend, Thailand issued an arrest warrant for a 27-year-old Muslim man called Abudusataer Abudureheman, also known as Ishan, from Xinjiang.
Abudusataer Abudureheman is reported to have left Bangkok for Bangladesh one day before the bomb blast, and is believed by police to have played a prominent role in the attack.
Thai authorities have already arrested two other suspects: Adem Karadag, whose nationality has yet to be verified, and Yusufu Meraili, who officials say is a Chinese national born in Xinjiang.
Xinjiang is home to a significant number of Uighur Muslims, and Chinese authorities have faced criticism for the perceived harsh restrictions placed on religion and culture in the region.
Thailand recently found itself in the spotlight following its forced repatriation of more than 100 Uighurs to China.
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