Manager Ron Washington said Francisco's biceps tendinitis will be reevaluated on Friday.
Francisco had a light throwing session before Wednesday night's game against Seattle, and reported less soreness in his arm. He had an injection Monday.
C.J. Wilson, who had 24 saves last season, will handle the closer's role in Francisco's absence.
Francisco, who last pitched Wednesday in Oakland, missed the entire 2005 season after elbow ligament replacement surgery. The right-hander became the team's closer last August when Wilson underwent season-ending elbow injury.
Francisco leads the Rangers bullpen with nine saves in as many chances and hasn't allowed a run in 14 appearances. He hasn't given up an earned run since Aug. 25, 2008, a stretch of 25 2-3 innings.