The wicketkeeper-batsman experienced pain in the gym prior to training and will be assessed ahead of the start of the match at 10pm on Thursday evening (UK).
Buttler, 29, would be replaced as wicketkeeper by Surrey's Ollie Pope, who played as a specialist batsman during the first Test defeat in Mount Maunganui.
Speaking in his pre-match press conference, captain Joe Root said: “Jos has tweaked his back in the gym. We’ll have to find out a little bit more information on that throughout today and tomorrow and see where he’s at.”
Root also confirmed he will take a final look at the pitch ahead of the toss before deciding on the team as England look to draw the two-match series.
He added: "There's a number of different combinations we could go with and I think a lot of that will rely on the surface. Trying to find the best combination which would take 20 wickets and then balancing that in terms of getting the batting where we want it to be. It could be an allrounder, we'll see."