The centre-back sustained the knock early on in the game after being caught by a challenge from Brazilian midfielder Romulo, and was forced to leave the pitch in just the 12th minute.
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Pique underwent further examination immediately after the match, and the club have now confirmed that the 25-year-old will be out of action for two to three weeks with a sprained foot.
The Spain defender will consequently miss the Liga match against Sevilla on September 29, and the trip to Benfica in the Champions League on October 3.
However, Barca are hopeful that Pique will regain match fitness in time for their Clasico encounter with Real Madrid three days later.