Robert, 24, has yet to be diagnosed, but his symptoms did not improve over the All-Star break. General manager Rick Hahn indicated he was hopeful Robert's stay on the injured list would be minimal but could not specify a timetable for his return.
Robert is expected to do some activity on the field on Saturday.
"You're always concerned," manager Tony La Russa said Friday afternoon. "It's foolish [to think], 'What's the big deal?' Because it is a big deal. Keep your fingers crossed. ... We'll see soon."
Hahn pointed to a couple of plays last week where Robert seemed slow to react to balls hit to him in center field, but he hadn't expressed any issues until he came out of last Friday's game.
"Interesting enough, it was affecting him more on the field than at the plate," Hahn said. "At this point his symptoms have not fully resolved."
The White Sox also activated catcher Yasmani Grandal from the injured list Friday.
Grandal, 33, has been on the IL since mid-June with lower back spasms. His return means the White Sox will carry three catchers as both Reese McGuire and Seby Zavala are out of minor league options and would be subject to waivers.
The White Sox have been impacted by injuries to key players the past two seasons but are close to full strength despite Roberts' absence.
"Everyone is going through it," La Russa said. "Everyone is missing key players. Most seasons you have some of this. This season there is quite a bit of it for everybody. The games still count."