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.
Montgomery (oblique) isn't expected to make his minor-league season debut until late April, James Fegan of The Athletic reports.
Montgomery has been invited to the major-league side of White Sox camp this spring.