According to Chief of the Indonesian National Police Badrodin Haiti, 17 of those arrested were directly linked to the Jakarta attacks last month while the remaining were members of three other radical groups.
He said a group led by an extremist called Hendro Fernando had received US$97,000 from Jordan, Iraq and Turkey, adding that it planned to launch attacks against Jakarta's main airport and the national police headquarters.
Another group headed by a person identified only as 'Helmi' planned to use a car bomb to attack the Jakarta police complex in the city's main business district, and a third group targeted traffic police.
He warned of terrorism attacks in the future because of other groups linked to Bahrun Naim in Syria.
The arrest followed a series of January 14 attacks in Jakarta that killed four civilians and four attackers.
Indonesia, the world's most populous Muslim-majority country, suffered several major bomb attacks by Islamic radicals between 2000 and 2009, including the 2002 Bali bombings that killed 202 people.