Menoncello, 24, played just six minutes of Toulouse's Champions Cup win over Exeter on Sunday before being forced off through injury.
Azzurri head coach Gonzalo Quesada will also be without scrum-half Martin Page-Relo, back-rower Sebastian Negri and Zebre full-back Lorenzo Pani for the games against South Africa, Argentina and Fiji.
The competition concludes the weekend of November 27-29 with a series of games to determine the final standings.
"We know that major challenges await us this year, starting with the injuries to several players who are very important for our team," ex-Argentina fly-half Quesada said in an FIR statement.
"But one year out from the Rugby World Cup, I also see these difficulties as a great opportunity to give playing time to some young players who represent the future of the national team.
"And, above all, to test our character by facing, for four consecutive weeks, four of the best teams in the world."