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.
'Obviously Messi is the best player in history and being compared to him means that you're doing things right, but I try to be myself': Barcelona star responds to comparisons with Argentine legend
'Darwin Nunez would be gold for Arsenal': Liverpool legend claims Gunners should have signed Uruguayan striker in January
