The authorities said they were not members of so-called Islamic State but had tried to make contact with the group.
The arrests were made in the southern state of Parana.
They come just over two weeks before the Olympic Games get under way in Rio de Janeiro.
Justice Minister Alexandre Moraes told a news conference that all those arrested were Brazilian. Two more suspects were being sought
A court in the southern state of Parana said there were indications that the group was planning to use weapons and guerrilla tactics to achieve its aim, Reuters news agency reported.
An emergency cabinet meeting has been called.
More than 80,000 police and soldiers will patrol Rio streets for the games which end on 21 August.
The federal government said last week that it was releasing an extra $24million (£18million) to beef up security ahead of the Olympics.
The International Olympic Committee recently concluded that Rio de Janeiro had overcome setbacks and is “ready to welcome the world” to the 2016 Olympics.
There have been fears over Rio’s readiness because of building delays, the Zika virus and political crises.