Hill landed on the 10-day injured list Saturday due to shoulder inflammation, AJ Cassavell of MLB.com reports.
Hill has struggled to start the season, striking out just one batter in 5.2 innings while giving up seven runs on 11 hits. He'll now miss potentially an extended period, though the team hasn't specified exactly when he's expected back. Ray Kerr was recalled to give the Padres another lefty in the bullpen in Hill's absence.