Moncada (adductor) will begin a rehab assignment with the White Sox's Arizona Complex League affiliate Tuesday and could rejoin the MLB club by the end of July, Scott Merkin of MLB.com reports.

Moncada will exclusively DH to start out his minor-league rehab stint, which will serve as his first in-game action since he suffered an adductor strain in early April. The veteran third baseman still has multiple checkpoints to clear before being reinstated, but he could be back before the calendar flips to August.