The influential 24-year-old was injured during Saturday's Premier League match against Wigan Athletic and would recuperate in Belgium, his country's football association said.
"Fellaini suffered a small tear at the juncture of muscle and tendon in the knee. The injury was revealed during a scan," a statement on the Belgian FA website said.
"Fellaini was injured last Saturday during the match between his club Everton and Wigan Athletic. He will be out three weeks.
"It has been agreed with his club Everton FC he will rehabilitate in Belgium during this period."
Belgium play Serbia in Belgrade on Friday before they take on Scotland in Brussels on Tuesday. The Belgians are second in Group A, behind Serbia on goal difference, on four points after two matches.
Fellaini will also miss Everton's match at QPR on October 21 and faces a race against time to be fit for the Merseyside derby against Liverpool a week later at Goodison Park.