Coach Lindy Ruff provided the update Saturday a day after the veteran defenseman left practice. Ruff said it's not clear how Rivet was hurt, but noted the player's throat started to swell.
Rivet visited a specialist and was told to spend two days resting before he can begin exercising, Ruff said.
A 14-year NHL veteran, Rivet had been limited during the first week of training camp while recovering from offseason shoulder surgery. He was on track to be ready for the season opener at Ottawa on Oct. 8.
The Sabres opened their preseason schedule Saturday night against Toronto.