The former captain has struggled with the problem for a number of months and a recent setback means that he will miss both the Test and limited-overs matches.
Todd Astle looks the most obvious replacement for Vettori following the decision to hand the all-rounder a first call-up to the national side.
Selector Kim Littlejohn said: "We have kept faith with the bulk of the players who took part in the recent winter tours and ICC World Twenty20.
"The one new face is Todd Astle. He has the ability to contribute in all three facets of the game and deserves his opportunity after a putting in consistent performances over a number of seasons."
Limited overs squad:
Ross Taylor (captain), Trent Boult, Andrew Ellis, James Franklin, Roneel Hira, Rob Nicol, Tom Latham, Brendon McCullum, Nathan McCullum, Kyle Mills, Adam Milne, Jacob Oram, Tim Southee, BJ Watling, Kane Williamson
Ross Taylor (captain), Todd Astle, Trent Boult, Doug Bracewell, Daniel Flynn, James Franklin, Martin Guptill, Chris Martin, Brendon McCullum, Rob Nicol, Jeetan Patel, Tim Southee, Kruger van Wyk, Neil Wagner, Kane Williamson