Alfano said he had ordered the expulsions after a "long and complex investigation" into a Facebook account which had posted "countless" videos and documents in support of the terrorist group Isis.
Police identified the owner of the account as a 28-year-old Macedonian living in Gorizia, northeastern Italy.
The man's two brothers-in-law, aged 31 and 28, along with their 52-year-old father and one of the brothers' wives, aged 32, were also expelled on Sunday for posting numerous extremist messages on social media sites.
Alfano said the group were "all fanatic followers of the self-proclaimed Caliphate" and that they had praised both terrorist attacks in Europe and the actions of Isis in Syria.
The group had repeatedly criticized their imam and the local Muslim community for being 'moderates' and open to western influences.
Since January 2015, Italy has expelled 121 Islamic extremists as part of its strategy of prevention, including 12 imams.