A video has been shown on TV showing armed men with the captured people and asking for Italian soldiers to leave Iraq.
Earlier on Tuesday, five Russian and three Ukrainian people taken hostage in Iraq were released, as were seven men from China.
Elsewhere US soldiers have arrested a helper of Shia cleric Moqtada Sadr.
Sadr is a man who doesn't want the US to have any part in what is going on in Iraq, and has an armed group called the Mehdi Army backing him.
It's not the first time the US have arrested an aide of Sadr, and last time lots of violence happened in the days afterwards.