Right-hander Jimmy Lambert was recalled from Triple-A Charlotte in a corresponding move and will start the second game of the double-header in Cleveland.
Kopech, 25, already had been on the bereavement list since last Thursday. The hard-throwing right-hander is 2-0 with a 1.78 ERA and 45 strikeouts over 31⅓ innings in 14 games, including three starts, this season.
Lambert, 26, made two relief appearances for the White Sox last season and did not allow a run. He has a 7.71 ERA in five starts with Charlotte this season.