Home Minister Zahid Hamidi said those arrested, the youngest just 14, were planning to attack police stations and army bases to gather weapons.
Two of the suspects had just returned from Syria, police said.
The government's tough and disputed new anti-terrorism laws are due to be debated in parliament this week.
The Bernama news agency quoted Mr Zahid as telling parliament that those arrested, who were aged between 14 and 44, were also planning to kidnap high-profile individuals. The targets were not named.
Mr Zahid said notes had also been found describing how to make bombs. The notes were written by an Indonesian executed for his role in the 2002 bomb attacks in Bali.
Two of those arrested were members of the army.
The new anti-terror laws have raised concern among human rights and opposition groups, who fear they may be used to stifle political dissent.
The new Prevention of Terrorism Act would permit indefinite detention without trial. The Special Measures Against Terrorism in Foreign Countries would permit the revocation of passports of Malaysians or foreigners suspected of terrorist activities.
Prime Minister Najib Razak said in November last year the measures were necessary to combat militant Islamist cells and "lone wolf" attacks.
He had previously pledged to abolish Malaysia's controversial sedition law, but at his party's annual congress in November said instead that it would be strengthened.
Why the controversy of Malaysia's sedition law?
Police in Malaysia say they have arrested 17 suspected militants who were believed to be planning terrorist attacks in the capital, Kuala Lumpur.