Padilla -- who has been on the DL since April 23 with an inflamed radial nerve in his throwing arm -- will take Billingsley's place in the rotation and start Saturday at Boston.
In his third and final rehab start Sunday, Padilla pitched for Triple-A Albuquerque and allowed six runs and eight hits in 5 2/3 innings.
Despite the shaky numbers, Torre said the right-hander is able to throw all his pitches and is ready to go. In four starts before going on the DL, Padilla went 1-1 with a 6.65 ERA. He last started for the Dodgers on April 22 in an 8-5 loss at Cincinnati.