Vidal returned for the first leg of Bayern's Champions League quarter-final triumph against Sevilla but was substituted after 36 minutes and aggravated his knee problem during training at the weekend.
A tweet posted by Bayern read: "Get well soon, @kingarturo23.
"Vidal underwent surgery on his knee yesterday, ruling him out for the rest of the season."
In a statement on their official website, Bayern declared the operation to repair Vidal's "rear lateral meniscus" to be a success.
The 30-year-old will have an extended off-season in which to recuperate after Copa America holders Chile missed out on a place at the 2018 World Cup.