A minor from Kosovo was also was detained to prevent him from interfering with the probe, police said. All had papers allowing them to live legally in Italy.
Up to three other Kosovars were also under investigation over their ties to those arrested, Adelchi D'Ippolito, Venice's chief prosecutor, told a news conference streamed online.
Police had been monitoring the group since last year. They tapped their phones, bugged their apartments and followed their online communications, and what emerged was "disturbing and worrying," D'Ippolito said.
The group had expressed an unconditional support for Islamic State, he added.