Smith sustained the injury during the team's December 29th matchup against the Ottawa Senators and had his surgery on Tuesday.
The 36-year-old has no goals and two assists through 15 games this season.
After the team released him following a tryout on September 28th, the team signed Smith to an official two-way, one-year contract for the season on November 24th.
Smith is now in his 16th season in the NHL. After being selected 27th overall in the 2007 NHL Draft, Smith would spend the first six years of his professional career with the Detroit Red Wings, making his debut during the 2011-2012 season.
Smith would spend the next five seasons (2016-2020) as a defenceman for the New York Rangers, before joining the Carolina Hurricanes for one (2021), the New Jersey Devils for two (2022-2023), then the Dallas Stars for one (2024) before joining the Blue Jackets.
In 741 career games, Smith has recorded 39 goals and 107 assists (146 points). He set a career high in goals (five) and assists (14) during his third year (2013) and has yet to surpass them since.