The Chilean suffered a setback on Sunday in his first training session since he sustained a knee injury against Sevilla earlier this month.
Vidal missed Tuesday's DFB-Pokal semi-final against Bayer Leverkusen, but the player will now be sidelined for the Champions League double-header with Real Madrid.
"Arturo Vidal underwent knee surgery in Augsburg on Monday," the Bavarians said in a statement.
"The loose body that had been diagnosed beforehand was removed. The attachment of the rear lateral meniscus which was damaged by the loose body was repaired.
"The season is over for Arturo Vidal."
Prior to missing the second leg against Sevilla through injury, Vidal had appeared in all but one of Bayern's Champions League games this season.