Australian media are reporting that the paceman has lost his battle to get match fit in time for this evening's encounter.
Boult missed the second test against England earlier this month due to the same injury and was replaced by Matt Henry for the drawn second test in Hamilton.
The Black Caps won their seventh series after beating the English comprehensively in the first test in Mount Maunganui.
Fox Cricket are reporting that Boult will be replaced by speedster Lockie Ferguson, who is set to make his debut.