The Belgium centre-back has been told to rest for up to 12 days following a scan on a calf strain in Manchester in midweek.
National captain Kompany will miss the Euro 2016 qualifier with Wales on Sunday and is now a major doubt for the Premier League game against Swansea on November 22 as well as the tie with Bayern at the Etihad three days later.
Belgium coach Marc Wilmots revealed the extent of the injury before last night's 3-1 friendly win over Iceland.
Wilmots said: "The news is bad and Vincent is out for at least 10 to 12 days so he can't play on Sunday.
"I told the team it's a shame but it's not a problem, there are solutions."
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