Sheary was placed on injured reserve by the Sabres on Monday with an undisclosed injury.
Even when healthy, Sheary was far from a lock to play on a nightly basis and will likely serve as a healthy scratch periodically once given the all-clear. In his 62 regular-season tilts last year for the Rangers, the 34-year-old winger notched seven goals, 11 assists and 81 shots while averaging 14:06 of ice time.