Giolito struck out six while pitching four innings of one-hit ball in Detroit.
“I’m concerned because he felt something,” manager Tony La Russa said.
Giolito departed with a 3-0 lead, but the Tigers rallied for a wild 5-4 win.
He made his third straight start on Opening Day for the White Sox. He was 11-9 with a 3.53 ERA last season.
“We got a lot riding on him,” La Russa said. “Getting checked and seeing what it is.”
The White Sox have been hit hard by injuries already. Third baseman Yoan 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 Yermin Mercedes (fractured left wrist).