The centerback will miss Friday's European Supercup when the Champions League winners play Europa League victor FC Porto in Monaco after tearing a muscle in his left leg, his Spanish club said.
The World Cup winner will miss Spain's international friendly against Chile in Geneva on Sept. 2 and a European Championship qualifying match against Liechtenstein four days later.
The 24-year-old Pique has been a regular in Pep Guardiola's squad since arriving from Manchester United in 2008, helping the Spanish champions to 11 major trophies including two European Cups.
Barcelona's backline, which is already without Carles Puyol, will be tested. Eric Abidal and Javier Mascherano are likely to fill in.