The Dutch international picked up the injury in Barca's 2-1 friendly defeat to Manchester United in Washington DC on Saturday, but will stay with the team as they continue their pre-season tour of the United States.
Afellay will miss the La Liga curtain-raiser against Real Madrid when the league champions take on King's Cup winners in the Spanish Super Cup on August 14 and 17.
The 2011/12 La Liga season kicks off on the weekend August 20-21.
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