The militants - all from a domestic cell affiliated with the Syria-based jihadist group - had amassed enough explosives to create bombs more powerful than those used in the 2002 Bali bombings, which killed 202 people, police say.
"They were helping plan a bomb attack against parliament, the national police headquarters, the embassy of Myanmar and several television stations," national police spokesman Rikwanto said in a text message.
Anger is growing in Indonesia and other parts of Muslim world over what has been described as the "ethnic cleansing" of Rohingya in Myanmar's Rakhine state.
Thousands of Muslims rallied in capitals across Asia on Friday demanding an end to the violence.
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In Indonesia, the world's largest Muslim-majority country, protesters urged their government to cut diplomatic ties with Yangon.
Indonesia's anti-terror unit Wednesday nabbed suspected bomb maker Rio Priatna Wibowo and seized a significant quantity of high-grade explosives from a laboratory west of the capital Jakarta.
His arrest led to the capture of two other suspected militants in different parts of the country, Rikwanto said today.
Indonesian police say it remains unclear when exactly the militants planned to carry out their assault, but that they had enough explosives to detonate a blast more than double that which levelled nightclubs in Bali in a fiery inferno.
All three were members of Jemaah Ansar Daulah, a local extremist outfit that has sworn allegiance to IS, Rikwanto said.