Another suspected terrorist was shot and killed by police during Sunday's attack on a police station in Medan, the capital of North Sumatra province.
The wife of the arrested man told police her husband had spent six months in Syria in 2013, said police spokeswoman Rina Sari Ginting, adding this was still being investigated.
Police believe the men were part of Jemaah Ansharut Daulah (JAD), an umbrella organization on a US State Department "terrorist" list which supports ISIS and has hundreds of Indonesian followers.
"We can see from the pattern of their attack that it is likely they belong to the JAD network," said Ginting.
There is concern about a rise of terrorism in Indonesia, which has the world's biggest Muslim population.
ISIS sympathisers have carried out a series of mostly low-level attacks over the past few years, and there are fears about the return of hundreds of Indonesians who have gone to Syria to support ISIS.
They appeared to be designed and printed by the suspect, she said.
Police believe the suspects had intended not only to kill police during Sunday's knife attack but also to seize their guns.
Out of 12 people being questioned in connection with the attack, one had been made a suspect and is alleged to have helped the attackers by surveying the police headquarters, she said.
Police were also investigating whether the attackers were linked to three suspected terrorists who were arrested on June 6 in the area by anti-terrorism police.
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