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.
"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)
