The announcement came a day after the US and Australian embassies had warned their citizens to avoid a popular Kuala Lumpur tourist area yesterday due to an unspecified security threat.
The detainees were planning to "attack important national assets, Western assets, and public spots," a statement by Deputy Inspector-General of Police Noor Rashid Ibrahim said.
The statement did not specify their nationalities, but Malaysian news outlets quoted Noor Rashid later telling reporters they were a Malaysian, a Syrian and an Indonesian.
Yesterday, the US and Australian embassies warned citizens to stay away from Jalan Alor, an outdoor dining strip in central Kuala Lumpur that is packed nightly with foreigners and locals.
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Malaysian news outlets quoted Noor Rashid saying the arrests were related to the Jalan Alor threat, and that the detainees were taken into custody on Thursday.
"The operation is a result from information obtained from suspects arrested previously," the police statement said.
Muslim-majority Malaysia practises a moderate brand of Islam and has not seen any notable terror attacks in recent years.
Authorities say dozens of Malaysians have travelled to Syria to fight for the radical Islamic State in its civil war there, and warn they may seek to return home and import its Over the past year, police have arrested numerous suspects whom they say were IS sympathisers plotting attacks.
Last month, police said 10 Malaysians were arrested for fostering suspected links with the Islamic State and planning attacks in the country.
Opposition lawmakers, however, say the terror arrests over the past year have been shrouded in secrecy, making it difficult to gauge the actual threat level.