Moore logged just over 4 minutes of ice time Tuesday and didn't play in the final two periods of New York's 3-2 win. The 33-year-old Moore, who played in the Rangers' first 11 games this season, sat out Thursday night when New York hosted the Buffalo Sabres.
Brandon Mashinter, a healthy scratch in the Rangers' previous three games, replaced Moore in the lineup. Mashinter's only game action this season was a four-minute stint against Philadelphia last week.
The Rangers are already missing top forward Rick Nash (concussion) and captain Ryan Callahan (broken thumb). Callahan took park in the team's morning skate Thursday for the first time since he was injured on Oct. 16. He wore a non-contact jersey, but could return in a week to 10 days.