The White Sox also transferred outfielder Luis Robert to the 60-day injured list, purchased the contract of right-hander Ryan Burr from Triple-A Charlotte and sent left-hander Jace Fry on an injury rehabilitation assignment to Charlotte.
Kopech is 2-0 with a 1.78 ERA in 13 games this season. He has worked two-plus innings in six of his 10 relief appearances. Under Major League Baseball rules, Kopech must remain on the bereavement list for a minimum of three days and not more than seven.
Burr is 1-1 with a 5.40 ERA, nine strikeouts and two saves over eight relief appearances with Charlotte this season.
Fry, who has been on the injured list since April 1 (retroactive to March 29) recovering from an offseason microdiscectomy, went 0-1 with a 3.66 ERA with 24 strikeouts over 18 relief appearances last season.
Robert has been on the injured list since May 4 with a Grade 3 strain of his right hip flexor suffered while running to first base on May 2 against Cleveland.