The White Sox optioned Leasure to Triple-A Charlotte on Friday.
Leasure earned a high-leverage role with a 2.52 ERA through his first 26 outings this season, but he'll head to the minors after giving up six runs in his past four outings. The right-hander is a decent bet to rejoin Chicago later in the summer, especially if the club offloads any bullpen pieces ahead of the trade deadline.