X-rays taken Thursday revealed the fracture.
Greene suffered the injury after being hit by a shot in the Devils' 1-0 victory over the New York Islanders on Nov. 25.
Mark Fraser started in Greene's place against Ottawa on Thursday night, and will likely continue to until Greene returns.
In 23 games this season, Greene has zero goals and nine assists.
Mike Mazzeo is a regular contributor to ESPNNewYork.com.