The move is retroactive to Saturday.
"It's a matter of how he responds to treatment over the next few days before we come up with an exact timetable," White Sox general manager Rick Hahn told reporters.
A two-time All-Star, Hendriks was not available for Monday's 9-5 win against the Detroit Tigers due to what the team said was a sore arm, but he did play catch before the game.
He is 1-2 with an AL-best 16 saves, a 2.81 ERA and 37 strikeouts in 25 appearances this season. A year ago, he led the league in saves with 38.
In other moves Tuesday, the White Sox reinstated right-hander Joe Kelly (hamstring) from the 15-day IL, recalled righty Davis Martin from Charlotte and optioned lefty Bennett Sousa to the Triple-A affiliate.