Rivet skated with the team Monday morning in preparation for the Sabres' game against Nashville but then was scratched later in the afternoon before a 2-0 loss to the Predators.
Coach Lindy Ruff said Rivet was hurt on a hit in Saturday's loss to Montreal. Nathan Paetsch dressed for only the seventh time this season, replacing Rivet.
It's not known what Rivet's availability will be when the Sabres begin a three-game road trip Thursday at Florida.
The Sabres did receive some good news: They welcomed back right wing Ales Kotalik. Kotalik had missed the last seven games after sustaining a hamstring injury against Columbus on Nov. 14.
At the time of his injury, Kotalik was playing on the top line with center Derek Roy and left wing Thomas Vanek. On Monday, Kotalik skated alongside Mark Mancari and Clarke MacArthur.
PREDATORS 2, SABRES 0: Jason Arnott snapped a scoreless tie eight minutes into the third period to help give Nashville the win in a game that lacked spark and excitement for the first two periods. The Sabres sent 30 shots at Predators goalie Pekka Rinne, but the rookie goalie turned aside each one. The Sabres lost for the second consecutive game and were blanked for the second time this season.