Former Manchester City forward Rolando Bianchi and defender Riccardo Colombo were slapped after being surrounded by a group of about 25 people, Torino's players said on the club's official website on Thursday.
The group then entered the restaurant where forward David Di Michele was celebrating his birthday and directed "slaps, threats of death and assaults at home, and pushes" at other players in front of their families, the statement said.
The fans are furious about the poor form of the team, who are 10th after being relegated from Serie A last season.
The AIC said it "expresses totally solidarity with the Torino players who suffered a vile ambush, attacked outside a restaurant after dinner with their families, and firmly condemns this shameful incident".
"The repetition of such appalling episodes will force the AIC to resort to appropriate acts of protest," it added on its website.
The Torino players also said they were considering giving a "strong signal" of protest.
Giancarlo Abete, the head of the Italian Football Federation, described the incident as "shameful."
The AIC said players of Serie A team Palermo and Serie B side Brescia had been victims of similar incidents recently.
Italy is trying to stamp out a serious hooliganism problem that has dogged the game in recent years. The government plans to introduce electronic supporter identity cards next season for fans to carry to away matches.
‘Maybe I’ll be signed by Wrexham, who knows? English football would suit me – if an offer came, I wouldn’t think twice, I’d go immediately’ Euro 2024 cult hero reveals his UK dream
‘Managing Leeds? It was an option that appeared, but it wasn’t the right timing. I decided it wasn’t a good idea to leave the club I was at mid-season’: Premier League boss admits to turning down opportunity to replace Jesse Marsch in 2023
