The Belgium international was unable to join up with the squad for their two World Cup qualifying games against Serbia and Scotland after sustaining the knock in the Toffees’ 2-2 draw at Wigan.
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"As you have probably seen and heard I am currently suffering from a knee injury," he told the club’s official website.
"Fortunately it is not too serious but I will have to miss the two games with Belgium.
"I am hoping to be back playing for Everton as soon as possible."
The Belgian Football Association yesterday released a statement confirming that the 24-year-old will undergo rehabilitation in his home country, and estimated he would be out of action for at least three weeks.
Fellaini has been an influential figure for David Moyes’ side so far this season, scoring three goals and helping guide the Toffees to fourth in the Premier League.