The defenseman was injured in the first period of a 2-0 loss at the New York Islanders on Saturday.
Werenski ranks third on the Blue Jackets with 16 points (six goals, 10 assists) in 26 games this season. Selected with the No. 8 pick in the 2015 NHL Draft, Werenski has 144 points (44 goals, 100 assists) in 263 regular-season games and 10 points (three goals, seven assists) in 19 Stanley Cup Playoff games.
Columbus (11-11-4) will play its first game without Werenski when it hosts the Arizona Coyotes at Nationwide Arena on Tuesday (7 p.m. ET; FS-O, FS-A, FS-A PLUS, NHL.TV).