The National Police's spokesman Rusdi Hartono said the suspects communicated through a WhatsApp group called the Iman Battalion.
"In that group, they discussed plots for the next practice (terrorist act), as well as discussed how to assemble explosives," Hartono said on Tuesday.
One was arrested in Gowa district and the other five were held in Makassar.
The police also seized an airsoft rifle which they used for war training, seven cellphones, and a motorbike.
A suicide bomb exploded at the Makassar Cathedral church, South Sulawesi, killing two of the perpetrators and injuring 20 others on March 28, when Christians in Indonesia were celebrating Palm Sunday, a Christian feast that falls on the Sunday before Easter.
The National Police's Chief General Listyo Sigit Prabowo said the two perpetrators were linked to the homegrown terrorist group Jemaah Ansharut Daulah.
In another development, the death toll from the tropical cyclone Seroja that recently hit Indonesia's province of East Nusa Tenggara was revised to 178 with 47 people still missing, according to the latest official data.
The death toll was revised from 179 as informed by the province's Deputy Governor Josef Nae Soi on Monday evening.
At a virtual press conference held by the country's disaster mitigation agency on Tuesday afternoon, the provincial official also said that the number of evacuees has decreased.
At least 7,895 people are still staying in temporary shelters compared to the previous number of evacuees at 34,838, according to him.
He also said that at least 259 people still suffered from injuries caused by the flash floods and landslides triggered by the cyclone earlier in April.
Floods and landslides also destroyed houses, public facilities, roads and bridges in the affected areas. - Xinhua