The attack occurred against La Stampa reporter Andrea Joly on July 20 as he was taking photos and videos of a party being held in front of the club.
CasaPound is a neo-fascist movement founded in Rome in 2003.
Turin prosecutors have opened a probe on aggravated private violence and lesions.
The people suspected of involvement in the attack and placed under house arrest were identified.
They are Euclide Rigato, 45, a taxi driver from Turin; Marco Berra, 35, from Cuneo; Igor Bosonin, 46, a former candidate for mayor in Ivrea near Turin; Paolo Quintavalle, 33, from Chivasso.
A fifth person is also under investigation in relation to the incident, Maurizio Galiano, 53, from Turin.
ANSA