About 18 percent of NHL regulars are sidelined by injuries, including all-stars such as Alex Ovechkin, Ilya Kovalchuk and Evgeni Malkin.
According to a source close to the Rangers, Dubinsky is expected to miss three weeks with a broken bone in his right hand.
Dubinsky, 23, in his fourth season, is 3-7-10.
Drury is out indefinitely with a concussion, the result of an open-ice hit by Flames forward Curtis Glencross in the Rangers' zone.
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The Rangers (10-7-1), who ended the three-game western Canada trip 1-2, will look for help from the Hartford Wolf Pack or elsewhere. Among the options: P.A. Parenteau, 26, a winger who had two points in two games in a recent call-up; center Corey Locke, who tied for seventh in points in the AHL last season; and Evgeny Grachev, a 19-year-old Russian center-forward in his first AHL season.
The Rangers - who are owned by Cablevision, which also owns Newsday - are very close to the $56.7-million salary cap and players on injured reserve or long-term injured (LTI) list count against the figure. A player expected to miss at least 10 games and 24 days with an injury can be listed as an LTI, and be covered by a replacement. Cap relief is granted only for the portion that exceeds the cap; when the injured player returns, the team must immediately comply with the cap.
Glencross felled Drury at the 49-second mark when he dropped his shoulder into the center's head while the unsuspecting veteran waited for a pass that never came near the Rangers' blue line. The officials were looking elsewhere, Glencross was not penalized, and coach John Tortorella was angry.
"It was a missed call. Obviously, they didn't see it," he said. "It should have been a five-minute major."
The Rangers were expected to seek a review from the league.
Asked if his team should have retaliated, Tortorella said: "I think a lot of guys didn't even see it. But we're here to win the hockey game; that's so early in the game."
Drury, 33, who has two goals and four assists but leads all NHL forwards in blocked shots in his 17th season and third with the Rangers, left the ice woozy.
Early in the second period, while on a penalty-kill, Dubinsky blocked a slap shot from Jay Bouwmeester with his right arm, winced and tucked it into his side, but continued to play until the puck was cleared.
The setbacks could cost Drury and Dubinsky an opportunity to make the roster of the U.S. Olympic team, which is to be announced Jan. 1.