A fourth person, a minor, was also detained in overnight raids carried out after it was established that the suspects had undergone "religious radicalisation", a police statement said.
Searches were conducted at 12 locations in the historic centre of the city, which is a magnet for millions of visitors from around the world.
La Repubblica newspaper reported that the suspects were heard on wiretaps celebrating the attack outside Parliament in London last week, and had downloaded manuals on hand-to-hand fighting and the use of knives.