People living within a 300-meter (yard) radius of the boarding house where the pressure cooker bomb was found were evacuated during the police operation.
Two men and a woman were arrested in the neighborhood, said National Police spokesman Boy Rafli Amar. A fourth suspect, a man, was arrested in the central Java city of Solo, said Jakarta Police spokesman Argo Yuwono.
Umar Surya Fana, the police chief of Bekasi, a Jakarta satellite city where the evacuated neighborhood is located, said two men were arrested shortly after leaving the boarding house. The woman was arrested in the boarding house.
Police believed they were planning to bomb the presidential palace during a guard-changing ceremony that is a tourist attraction in Jakarta, he said.
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The woman's will, which was found during the counterterrorism operation, stated her desire to take part in "amaliyah," an Arabic term used by extremist groups for attacks or suicide bombings.
Police said those arrested are suspected to be part of a militant network responsible for a bomb-making lab raided last month in West Java province that was operating under the direction of Bahrun Naim, an Indonesian fighting with the Islamic State group in Syria.