The team announced the move on Friday night.
Musgrove's 1.59 ERA ranks second in the majors and he is 8-0 on the season, tied with four others for the major league lead in wins. He has recorded a quality start in each of his 12 appearances, becoming the seventh pitcher since 1994 to begin a season with at least that many in a row.
Musgrove worked seven innings on Thursday as the Padres beat the Cubs 6-4 at Wrigley Field to complete a four-game sweep. He allowed two runs on nine hits, striking out nine and walking none.
San Diego recalled right-hander Reiss Knehr from Triple-A El Paso to take Musgrove's place on the roster.