The 23-year-old was injured in the second period of Tuesday's preseason game against the Sabres. He underwent an MRI on Wednesday that revealed a second-degree sprain of the medial collateral ligament.
Jones was a first-time All-Star in 2017 and was selected again last season but missed the game due to illness. He finished last season with 16 goals and 41 assists for a Columbus team that had 97 points in the regular season. The Blue Jackets lost to the Cup-winning Capitals in the first round of the playoffs.
Jones was a first-round selection of the Predators in 2013 and was traded to the Blue Jackets for center Ryan Johansen in 2016.
The Blue Jackets open the regular season Oct. 4 at Detroit, then play their home opener the next night against Carolina.
The Associated Press contributed to this report.