The 28-year-old, who has played 27 of Barcelona's 32 games this season, left the pitch on a stretcher in the eighth minute of the match following a challenge from Nicolas Escalante.
The club did not give a timeframe for the Spain international's return.
Barcelona are already without injured midfielder Andres Iniesta.
They host Real Sociedad on Thursday in the Copa del Rey quarter-final second leg, holding a 1-0 advantage from the first-leg.
Barcelona, who are third in La Liga, travel to Real Betis on Sunday and face Paris St-Germain on 14 February in the Champions League last 16.
Barcelona midfielder Sergio Busquets has been sidelined after spraining his right ankle in Sunday's 4-0 win at Eibar.