Klein, a right shot, has spent time paired with Marc Staal, Keith Yandle and Ryan McDonagh this season. The way Dan Girardi and Dan Boyle have struggled (see: here and here) on the right side, you could make the argument that Klein was the last defenseman they could afford to lose. (You may not win the argument, but you could sure make it.)
With Klein out, Dylan McIlrath will get back into the lineup tomorrow in Brooklyn.
Currently, the Rangers have just six healthy defenseman on their roster.