Prior to the series opener at Toronto, the team also placed right-hander Lucas Giolito on the bereavement list.
Kelly, 34, is 0-1 with a 10.13 ERA in three appearances. He went on the IL on April 10 with a right groin strain.
Giolito, 28, is 1-2 with a 4.50 ERA and 28 strikeouts in five starts. He will be out for a minimum of three days.
White Sox reinstate Joe Kelly; place Lucas Giolito on bereavement list