Justice Minister Alexandre de Moraes said in the capital, Brasilia, that 10 suspects had been detained and two more were being sought. All are Brazilian, and one is a minor. The gender of the people was not given.
Police acted because the group discussed using weapons and guerrilla tactics to potentially launch an attack during the Olympics, which begin August 5, Moraes said.
However "they were complete amateurs and ill-prepared" to actually launch at attack, Moraes said. "A few days ago they said they should start practicing martial arts, for example." Still, Moraes said even disorganised groups should be taken seriously.
Moraes said they had all been "baptised" as Islamic State sympathisers online and that none had actually travelled to Syria or Iraq, the group's stronghold, or received any training. Several were allegedly trying to secure financing from the group, known by the acronym ISIS.
The justice minister added that one of the suspects communicated with a Brazilian store in an alleged attempt to by an AK-47 assault rifle, apparently the most concrete action taken toward a possible attack.
Security has emerged as the top concern during the Olympics, including violence possibly spilling over from Rio's hundreds of slums. Authorities have said they will be prepared and that some 85,000 police and soldiers will be patrolling during the competitions.