Sidelined since April 28 because of inflammation in his right elbow, Jones experienced discomfort during a throwing session last week.
General manager Rick Hahn said the issue stems from Tommy John elbow surgery Jones had in 2014. Hahn said scar tissue formed around the nerve and caused the irritation.
Hahn said Jones is expected to make a full recovery by the start of spring training.
Jones had a 2.31 ERA with 15 strikeouts and six walks in 11 appearances this year. He is 20-10 with a 3.12 ERA over six seasons with the White Sox.
Information from The Associated Press was used in this report.