Beckett hurt the outside of his thumb when it was hit by an opening clubhouse door about 10 days ago. To that point, Beckett was having a healthy recovery from last year's thoracic outlet syndrome surgery.
In his last start Saturday night, Beckett was charged with five runs in three innings, allowing three home runs.
Beckett struggled through a bullpen session on Wednesday, restricted to throwing fastballs. As the fifth starter, Beckett is not expected to make the trip to Australia or a regular-season start for the Dodgers until the middle of April because of numerous days off in the schedule.
Ken Gurnick is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.