Montgomery went 1-for-2 with a two-run home run in Saturday's Cactus League loss to the Cubs.
White Sox general manager Chris Getz said Thursday that he expects Montgomery to be the team's shortstop at some point this season, Scott Merkin of MLB.com reports.
The White Sox selected Montgomery's contract from Triple-A Charlotte on Tuesday, James Fegan of SoxMachine.com reports.
Montgomery is slashing .222/.335/.370 with seven home runs, four steals and a 28.2 percent strikeout rate in 57 games for Triple-A Charlotte.
The White Sox reassigned Montgomery to minor-league camp Monday, LaMond Pope of the Chicago Tribune reports.
The White Sox promoted Montgomery from High-A Winston-Salem to Double-A Birmingham on Monday, James Fox of SoxMachine.com reports.
Montgomery (oblique/back) will begin a rehab assignment with the White Sox' Arizona Complex League affiliate Monday, Scott Merkin of MLB.com reports.
Montgomery (oblique/back) has begun baseball activities at extended spring training, James Fegan of The Athletic reports.
White Sox general manager Rick Hahn said Thursday that Montgomery (oblique) is now also dealing with a mid-back strain, Scott Merkin of MLB.com reports.
Montgomery (oblique) is expected to get a brief tuneup at High-A Winston-Salem once healthy before heading to Double-A Birmingham, Jim Callis of MLB.com reports.