The White Sox reassigned Barlow (shoulder) to minor-league camp Wednesday, Vinnie Duber of AllCHGO.com reports.
Barlow will be sidelined indefinitely after being diagnosed with right shoulder soreness Thursday, Scott Merkin of MLB.com reports.
Barlow signed a minor-league contract with the White Sox on Friday.
The Royals outrighted Barlow to Triple-A Omaha on Sunday after he cleared waivers.
Barlow was designated for assignment by the Royals on Friday.
Kansas City claimed Barlow off waivers from the Rangers on Friday and optioned him to Triple-A Omaha.
Barlow was designated for assignment by the Rangers on Sunday.
Barlow was optioned to Triple-A Round Rock on Thursday, Evan Grant of The Dallas Morning News reports.
Texas reinstated Barlow (illness) off the 15-day injured list Wednesday.
Barlow (illness) began a rehab assignment with Triple-A Round Rock on Tuesday and struck out one over a perfect inning of relief in an appearance against Salt Lake.