Chicago also designated first baseman/designated hitter Yonder Alonso for assignment, purchased the contract of left-hander Ross Detwiler from Triple-A Charlotte and recalled outfielder Daniel Palka from Triple-A.
Anderson suffered a nasty right ankle sprain while making a defensive play in a loss at Boston on Tuesday evening. Anderson has 11 homers, 37 RBIs and a slash line of .317/.342/.491 in 70 games.
Alonso had struggled mightily, hitting .178 with seven homers, 27 RBIs and a .576 OPS in 67 games. The White Sox acquired him from the Indians in a trade in December.
Detwiler, 33, will start for the White Sox against the Twins on Friday evening. He was 1-2 with a 3.98 ERA in eight starts at Triple-A this season. He signed with the White Sox as a minor league free agent on May 9.
Palka made the White Sox's roster for Opening Day before being demoted after prolonged struggles, as he hit .029 (1-of-35) to open the season. He had 27 homers as a rookie for the White Sox in 2018. Palka hit .271 with 16 homers and 42 RBIs in 59 games at Triple-A before being recalled.