The Spain midfielder lasted just nine minutes of the 2-1 victory in Seville before being replaced by Alexis Sanchez.
A Barca statement read: "FC Barcelona's medical services have confirmed that Cesc Fabregas has torn the bicep femoris in his left thigh.
"He'll be sidelined for three to four weeks. Therefore, he'll miss the team's last three games in 2012 - the two Liga matches against Atletico Madrid and Valladolid and the away leg of the Copa del Rey against Cordoba.
"He could also miss the first games of 2013, against Espanyol and the return leg of the Cup at the Camp Nou."
Another concern for coach Tito Vilanova is the fitness of veteran skipper Carles Puyol, who was taken off at half-time at Betis with what the club said was "pain in his right leg".
Lionel Messi scored twice for Barca - his 85th and 86th goals of the season to beat Gerd Muller's record of 85 in a calendar year - as the Catalans retained their six-point advantage at the top from Atletico Madrid.