The midfielder has struggled with the problem for a number of months and has opted to go under the knife in his bid to find a permanent solution
The 26-year-old had an orthopaedic consultation on Tuesday in Barcelona and after that initial procedure it was decided the midfielder would go under the knife.
Vidal missed Juve's 1-0 win over Atalanta as the club celebrated winning a third straight Serie A title and will be absent for the final two fixtures of the season against Roma and Cagliari.
However, the player's surgeon, Ramon Cugat, remains confident the midfielder will be ready in time for the World Cup.
He said: "Arturo Vidal underwent keyhole surgery of his lateral meniscus in his right knee on Wednesday.
"Surgery was the best option and he will receive the best possible post-operative care. I would not rule him out of representing Chile at the World Cup, we are optimistic.
"If there was no World Cup then he would concentrate solely on his rehabilitation alone but the tournament adds a little pressure. The most important thing is his recovery."
Vidal has scored 20 goals for Juventus this season, meaning he is the club's second highest goalscorer behind Carlos Tevez.
Chile will be desperate their star man is ready in time for the tournament in Brazil as they prepare for a tough group containing Spain, Netherlands and Australia.