The 30-year-old Vidal limped out of training with a knee injury on Sunday and underwent minor surgery on Monday.
Bayern coach Jupp Heynckes had hoped Vidal could be fit for their European clash against Real next Wednesday or the return leg in Madrid on May 1.
But Bayern revealed Tuesday the injury is worse than first thought. A loose piece of the knee joint was removed and Vidal's meniscus was repaired, said a statement.
"Arturo Vidal will be out for the rest of the season," Bayern said.
Losing the tough-tackling midfielder for forthcoming key games is a blow to Bayern's hunt for the treble including Tuesday's German Cup semi-final against his old club Bayer Leverkusen.
A cup victory in Leverkusen would put Bayern in the May 19 final in Berlin -- another step towards repeating their 2013 treble.
The Bavarian giants have already secured a sixth consecutive Bundesliga title, holding a massive 20-point lead over Schalke at the top of the table with four games remaining.
Meanwhile, Bayern have announced they will play pre-season friendlies against Paris Saint Germain in Klagenfurt, Austria, plus games against Juventus and Manchester City in July on a tour of the USA.
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