The 26-year-old suffered the blow in his country's 1-0 win over South Korea in a Group H game on Thursday.
Belgium manager Marc Wilmots said: "Anthony won’t play again at this World Cup but will stay with our team."
Wilmots also has fitness concerns over captain Vincent Kompany and fellow central defender Thomas Vermaelen ahead of Tuesday’s last-16 clash with the USA in Salvador.
Manchester City skipper Kompany is nursing a groin problem, while Arsenal's Vermaelen only started running on Thursday after injuring his thigh against Russia.
Another defender Laurent Ciman is also doubtful for next week's clash with a groin complaint.
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