The Predators announced the trade Wednesday before heading to Vancouver for a four-game road swing.
Del Zotto, 23, has 11 points in 42 games for the Rangers averaging 17 minutes, 44 seconds of ice time per game. The 6-foot, 195-pound Del Zotto was the 20th overall choice by the Rangers in the 2008 draft, and he has 121 career points in 292 career NHL games.
Klein, 29, was the 37th choice overall in 2003 by Nashville and has played 403 games in nine NHL seasons. He has three points in 47 games this season and ranks 22nd in the NHL with 94 blocked shots.