The team captain is coming off a season in which he scored a career-low 14 goals and 32 points as the Rangers failed to advance to the playoffs.
A 2-1 shootout loss in the season finale to the Flyers left the Rangers in the Eastern Conference's ninth spot.
"The only thing worse than going through that as a team would be not learning from it," Drury said last week, according to the team's website. "When you go through something bad as a team and you don't learn from it, and you don't come out better for it, then that's strike three as far as I'm concerned."
Drury, 34, will miss the regular season's first four games as his left index finger heals.
"It's a tough break for him because he was skating well and in great shape," Rangers forward Vaclav Prospal said, according to the New York Daily News.