The forward was listed as day to day Tuesday before being downgraded Wednesday.
Sheary has three points (two goals, one assist) in three games this season. He had 34 points (14 goals, 20 assists) in 78 games with Buffalo last season after being acquired in a trade with the Pittsburgh Penguins on June 27, 2018.
"As soon as it's 'He cannot play,' we just move on and that's parked until that player returns, and then we make the best with the group we have," Sabres coach Ralph Krueger said after the morning skate Wednesday. "We have strong support up front with players in Rochester (of the American Hockey League), so we feel fine dealing with injuries, for sure."
Evan Rodrigues, who was a healthy scratch in each of the first three games this season, is expected to take Sheary's spot against the Montreal Canadiens on Wednesday (7 p.m. ET; SN, MSG-B, RDS, NHL.TV). Rodrigues had an NHL career-high 29 points (nine goals, 20 assists) in 74 games with Buffalo last season.
"I think we spoke about it before the season that Evan was left out of the lineup not because he wasn't performing or wasn't strong in what he does," Krueger said. "It was the way we put the puzzle together, and now the puzzle gets a bit of a remix. He'll have an opportunity today to play on the power play. He'll be an important player for us right out of the hop ... we have a long season ahead and there's always going to be somebody in that position. It happened to be him, but he's ready to go tonight."
NHL.com Independent Correspondent Heather Engel contributed to this report