The three boys, detained between April and June, had been "self-radicalized" online, adopting violent extremist ideologies, the Internal Security Department (ISD) said.
They are held under the Internal Security Act, which allows for detention without trial.
One of them, a 14-year-old student, is accused of planning a stabbing attack at his school, the ISD said.
Drawn to the jihadist ideology of the Islamic State group, he allegedly intended to target "non-Muslim teachers and schoolmates" and livestream the attack.
He had initially tried to acquire a gun but dropped the plan because of Singapore's strict firearm laws, and considered making a bomb but lacked the funds for it, the ISD said.
The boy idolized mass shooters, and was a fan of first-person shooter games on online platform Roblox, according to the security agency.
In another case, a 19-year-old tertiary student allegedly planned knife attacks against soldiers at an air base and LGBTQ students at his school.
The third suspect, a 15-year-old boy, was in the "early stages" of planning a bomb attack, the ISD said.
"Though their cases are not related, all three were self-radicalized online by violent extremist ideologies, and had made preparations to conduct local attacks," it said.
"These three cases drive home the severity of the youth radicalization threat in Singapore."
Last year police detained an 18-year-old who allegedly planned to livestream an attack on a mosque in Singapore with homemade guns, knives and molotov cocktails.
A 2024 government report on terrorism threats flagged youth radicalization as "a particular concern", with 13 of the 52 cases of "self-radicalized" individuals identified at the time by the security agency involving people aged 20 or younger.