Wood has not played worldwide cricket since suffering another ankle injury in July 2017, but he did feature in England's warm-up 50-over game against a Cricket Australia XI and finished with figures of 0-68 off his 10 overs.
England test squad: Joe Root (c, Yorkshire), Moeen Ali (Worcestershire), James Anderson (Lancashire), Jonny Bairstow (Yorkshire), Stuart Broad (Nottinghamshire), Alastair Cook (Essex), Mason Crane (Hampshire), Ben Foakes (Surrey), Liam Livingstone (Lancashire), Dawid Malan (Middlesex), Craig Overton (Somerset), Ben Stokes (Durham), Mark Stoneman (Surrey), James Vince (Hampshire), Chris Woakes (Warwickshire), Mark Wood (Durham).
"People are saying that Test cricket's becoming less important, but as players I don't think that's true at all".
"Unfortunately, they miss out on selection for New Zealand".
Livingstone impressed for Lancashire last season, scoring 803 runs at an average of 47.24, and was one of the best performers on the recent Lions tour to Australia.
Meanwhile, batsman Livingstone has been rewarded in the wake of his good form with Lancashire and for his good performances with the England Lions in the last couple of years.
"We are particularly impressed with the way he bats against spin and is equally adept against the seamers, " said Whitaker.
"He is a very talented and tough cricketer who has the ideal qualities and character to be successful in the Test arena".
Stokes, 26, hasn't played for England since an incident outside a Bristol nightclub a year ago, that resulted in an alleged assault, with the all-rounder stood down for the recently concluded Ashes series as a result.
"Mark is now back to full fitness and is looking forward to being part of our Test plans".
"Should the ECB Board receive formal confirmation that Stokes has either been charged or that he will face no charges, they would convene within 48 hours to make a decision on his availability for the team at that stage".
Ballance is the sole casualty among the batsmen following the 4-0 Ashes hammering - despite not playing in any of the Tests.
Mark Wood says he wants to be England's "X-factor bowler" after being recalled to the Test side for the tour of New Zealand in March.
The two games Test series will be played between 22nd March and 3rd April with Auckland and Christchurch being the venues.