The Rangers made the announcement Thursday, one day after Klein was injured with 19 seconds remaining in New York's 3-1 victory on Washington. Klein returned to New York to be re-evaluated by team doctors.
All the Rangers said Thursday was that the 30-year-old defenseman would be sidelined because of an upper-body injury.
New York, which took over first place in the NHL standings on Wednesday, has 16 games left in the regular season over the next four weeks. The Rangers' final game before the playoffs is at Washington on April 11.
Klein has played well this season, scoring nine goals and adding 17 assists with a plus-24 rating while playing in 65 of the Rangers' 66 games. His goals, four game-winning goals, and points are all career bests.
Matt Hunwick will likely replace Klein in the lineup. He has been a healthy scratch the past seven games and has played in only 40 games this season, recording no goals and eight assists.