Rosli bin Hamzah, 50, and Mohamed Omar bin Mahadi, 33, are being held under the Internal Security Act, which allows for detention without trial, the Ministry of Home Affairs said in a statement.
Rosli, who worked as a car washer, "became convinced that ISIS militants were fighting for Islam and that their beheading of 'enemies' was religiously permissible," the ministry said, referring to the Islamic State group by another name.
He "was keen to travel to Syria to fight for ISIS," the statement said, adding that he had researched how to travel to the war torn country.
"He was prepared to die a martyr," it added.
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Singaporean officials have repeatedly warned that the city-state -- a key US ally in the region -- is a prime target for IS militants.
Earlier this month, Indonesian police arrested six suspected militants over a plot to launch a rocket attack on an up-market Singapore waterfront district from the nearby Indonesian island of Batam.
The alleged leader of the group is accused of planning the attack with a leading Indonesian militant, who is believed to be fighting with the IS group in Syria.