General manager Mike Barnett said Reinprecht likely would not need surgery to repair the injury.
"I'm one of those guys who has to pick up for the loss of him," Roenick told reporters. "I look forward to the challenge. I look forward to more ice time. Playing with Doaner and [Sjostrom], that's going to be a good thing for me."
Reinprecht had a career-best five points in the Coyotes' 6-3 season-opening victory against the Islanders, but hasn't scored a point since.
"It's tough," Sjostrom told The Arizona Republic on Saturday. "He's a great player and a leader for us. It's tough to replace a leader like that, but we're just going to have to do it."
The Coyotes fell to 1-4 on the season, last place in the Pacific Division, with their 4-1 loss to the Predators on Saturday.