Giolito is expected to miss his next two starts, according to La Russa, after leaving his season-opening start on Friday because of abdominal tightness on his left side.
Giolito struck out six while pitching four innings of one-hit ball in Detroit.
"Optimistically, maybe a couple of starts,'' La Russa said Saturday of Giolito's estimated time out. "We're going to miss him.''
Giolito felt discomfort during three consecutive pitches and notified the coaching staff after the inning. He departed with a 3-0 lead, but the Tigers rallied for a wild 5-4 win.
"From my understanding, it's a random, freak, weird thing,'' Giolito said Saturday. "It doesn't happen to baseball players very often. ... I'm very optimistic this won't affect my season too much.''
The White Sox have been hit hard by injuries. Third baseman Yoán Moncada (strained right oblique) was placed on the 10-day injured list on Thursday along with pitchers Ryan Burr (strained right shoulder strain), Joe Kelly (right biceps nerve injury), Lance Lynn (right knee surgery) and Garrett Crochet (left elbow surgery) and outfielder Yermín Mercedes (fractured left wrist).
The Associated Press contributed to this report.