In December, Wagner signed a deal with Yorkshire to play the first ten games of the County Championship season, though now appears unlikely to be fit for their opening fixture against Leicestershire on April 6.
"We all know how much playing Test cricket for New Zealand means to Neil and we are all disappointed to see him side-lined like this," New Zealand coach Gary Stead said. "The fact he was still hoping to play on, carrying these injuries shows you just how determined he is to try and give his all for the team.
"Doug is a skilful bowler who has been in strong form for the Central Stags across formats this season. We believe his skills will complement the rest of the bowlers we have in the group going into the next Test."
Bracewell, 32, had last played a Test in 2016. In addition to the three fast bowlers still playing the first Test - Tim Southee, Matt Henry, and Blair Tickner - New Zealand also have right-armer Scott Kuggeleijn in the squad. Where Kuggeleijn only made his Test debut last month, Bracewell brings substantially more experience, having played 27 Tests where he has bagged 72 wickets.
"We think it's important for Will to keep getting cricket under his belt," Stead said. "With the timing of this round and the next Test we thought it was a good opportunity to get him on the park and have time in first-class match conditions."