The Sabres provided the update in a news release issued Monday, before their home game against the Carolina Hurricanes. The team did not disclose the nature of the injury.
The Sabres have already been eliminated from the playoffs, and close their season hosting Pittsburgh on Saturday.
Weber had missed two games since being hurt in a 4-3 win against Toronto on Wednesday. He's played five-plus seasons with the Sabres, and was voted the team's Masterton Trophy nominee for exemplifying qualities of perseverance, sportsmanship and dedication to hockey.
He had a goal and six assists in 64 games this season.