Burr will be re-evaluated in two weeks. He has posted a 4.58 ERA in 16 relief appearances this season.
In a corresponding move, Chicago recalled reliever Jose Ruiz from Triple-A Charlotte. Ruiz, 24, has a 5.11 ERA in 13 relief appearances across two stints with the White Sox this season.
The White Sox have a busy Tuesday ahead of them, as they'll continue a suspended 1-1 tie in the fifth inning against the Royals at 4:40 p.m. at Guaranteed Rate Field before playing their originally scheduled game in the evening.