The Spain international, who has been in excellent form over recent weeks, had to be replaced by Alexis Sanchez after pulling up in the ninth minute.
He will miss Barca's remaining three games of 2012 - the league matches at home to Atletico Madrid and away to Real Valladolid and the first leg of the King's Cup last 16 tie at second-division Cordoba, the club said in a statement on their website.
Fabregas may also be sidelined for the home game against Espanyol on January 6 and the return leg of the cup tie three days later, they added.
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