Bresnan's elbow problem means he will be rested, handing Warwickshire's Woakes a chance to stake his claim for the Ashes series against Australia later this year.
The other 14 players were all part of the England squad which won the recent away test series in India.
Woakes, 23, made his senior international debut in a Twenty20 game against Australia in 2011 but national selector Geoff Miller said this was a chance for him to broaden his experience in the longer format.
"With Tim Bresnan unavailable while his elbow is assessed there is a good opportunity for Chris Woakes to gain further experience in the international environment," Miller said in a statement from the England and Wales Cricket Board (ECB).
"Woakes has impressed on the England Performance Programme and with England Lions and Warwickshire in recent years as well as with England in the limited overs formats."
Bresnan underwent elbow surgery in 2011 and has struggled to recapture his best form, failing to take a wicket in the two tests he was selected for in India.
"We have a busy international summer ahead of us and the medical team felt this was an ideal opportunity for Bresnan to take some time out to ensure his elbow is functioning effectively," Miller said.
The first of the three tests against New Zealand starts in Dunedin on March 6.
England test squad: Alastair Cook (capt), James Anderson, Jonny Bairstow, Ian Bell, Stuart Broad, Nick Compton, Steven Finn, Graham Onions, Monty Panesar, Kevin Pietersen, Matt Prior, Joe Root, Graeme Swann, Jonathan Trott, Chris Woakes.
