Musgrove (elbow) threw a "light" bullpen session Monday, per MLB.com.
Musgrove (elbow) played catch Friday, Jeff Sanders of The San Diego Union-Tribune reports.
The Padres placed Musgrove on the 15-day injured list Sunday with right elbow inflammation.
Musgrove (3-2) got the win Sunday over the Blue Jays, allowing three runs on five hits while striking out three over seven innings.
Musgrove (1-2) was handed the loss Tuesday against the Cubs, allowing four runs on five hits and three walks over 4.0 innings. He struck out five.
Musgrove will start for the Padres on Friday against the Giants, Dennis Lin of The Athletic reports.
Musgrove allowed five runs on seven hits and two walks while striking out two batters over 2.2 innings in a no-decision against the Dodgers on Thursday in the second game of the Seoul Series.
Musgrove is scheduled to start the Padres' second game of the regular season March 21 versus the Dodgers in Seoul, South Korea, MLB.com reports.
Padres manager Mike Shildt last last week that Musgrove (shoulder) will not have any limitations in spring training, Kevin Acee of the San Diego Union-Tribune reports.
The Padres transferred Musgrove (shoulder) to the 60-day injured list Saturday.