Inspector-General Khalid Abu Bakar said Saturday that the European was arrested in Island state Penang while working as a part-time English tutor.
"He had joined al-Qaeda previously and was involved in terror activities in Afghanistan and Bosnia," Bakar said in a statement.
Four of the detainees were foreign nationals, while one was a Malaysian.
The Indonesian and Malaysian are "suspected of acting as facilitator to organize individuals from Malaysia and some Southeast Asian countries to join the Islamic State in Syria," using an alternative acronym for Daesh.
The statement said that the suspects -- all men -- were detained in five separate operations by the police's counter-terrorism unit between Nov. 17 to Dec. 1 in five different states nationwide.
All will be investigated under the Security Offences Act ( Special Measures) 2012 (Act 747) and the Immigration Act 1959/63.
Malaysia is on alert after Thai police confirmed Friday that the Russian intelligence service had warned of a possible attack on Russian assets in Thailand -- Malaysia's southern neighbor -- by Daesh-linked militants.
The previously unconfirmed memo had asked police to investigate claims that ten Syrian nationals with links to Daesh had entered Thailand with the intention of carrying out attacks on Russians in the popular tourist resorts of Pattaya and Phuket.
Malaysia has detained more than 130 people suspected of links with Daesh or other militant groups since last year.
