The 30-year-old Chile international is now sidelined for Tuesday's German Cup semi-final against Bayer Leverkusen and is also unlikely to make their Champions League semi-final first leg against Real Madrid next week.
Bayern are chasing a treble of titles having already secured the Bundesliga crown.
"He slipped and turned his knee," Heynckes said of Vidal's injury in training on Sunday.
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"I talked with the doctor. He did a scan. Arturo will need to undergo a minor arthroscopic surgery. He is already on his way to Augsburg. He is now ruled out for the short-term for sure."
(Reporting by Karolos Grohmann; Editing by Christian Radnedge)
