Tallinder was hurt in Buffalo's 3-0 victory over the New York Islanders on Thursday night, and missed Buffalo's 5-4 shootout loss to Atlanta on Saturday, the Sabres' first of the season.
It is the same arm he broke in a collision along the boards in Game 3 of last season's Eastern Conference finals against Carolina.
"It's tough," Sabres coach Lindy Ruff said. "I'm disappointed for him because he was playing real well for us, and now the same thing happened. I know how frustrating it is."
Tallinder has two goals and two assists in 10 games this season, and ranks second on the team in averaging 20:45 of ice time per game.
Rookie defenceman Nathan Paetsch, who has been a healthy scratch since the start of the season, replaced Tallinder in the lineup in Buffalo's loss to Atlanta that stopped the Sabres' record-tying 10-game winning streak.
"For his first game, and for the type of game he got thrown in, I thought he did a real nice job for us," Ruff said. "He's worked extremely hard in staying ready."
Paetsch made his pro debut appearing in two games last season, including Buffalo's loss to Carolina in Game 7 of the Eastern Conference finals.