The team recalled right-hander Juan Minaya from Triple-A Charlotte in a corresponding move.
Jones will be re-evaluated after six days without throwing, according to manager Rick Renteria, who told reporters he doesn't expect the DL stay to be lengthy.
"The MRI was good," Renteria said. "The diagnosis is not related to the elbow -- more muscular."
Jones had Tommy John surgery to repair the ulnar collateral ligament in his right elbow in 2014.
Jones, 32, retired one of three Cleveland Indians batters he faced Tuesday, allowing a double and a walk. He has a 4.01 ERA in 27 games this season, with 27 strikeouts in 24 2/3 innings.
For his career, Jones has a 3.20 ERA in 265 games, all in relief.
Minaya rejoins the White Sox after being optioned to Charlotte following a one-day stint with the team last week. The 27-year-old has allowed four runs on three hits in 3 1/3 innings with Chicago this season, walking nine.
--Field Level Media