Kompany was seen limping towards the end of the defeat on November 5 and missed the draw with QPR three days later.
Belgium coach Marc Wilmots was hoping to be able to call on Kompany for their Euro 2016 qualifier against Wales but admitted that it is now out of the question.
"I received a call from Vincent earlier," he told Belgian broadcaster RTBF.
"He is out for Manchester City for 10 to 12 days, so is unavailable for Sunday. It's a shame but there is no problem, there are only solutions."
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