Jamieson, 28, had been in line to play at least one of the upcoming Tests having not feature in international cricket since June when he initially picked up the back injury in England.
However, scans ahead of the opening match in Mount Maunganui have revealed another fracture and Jamieson will return to Christchurch for further assessment.
"It's really gutting for Kyle to have this happen after he'd put so much hard work in to getting himself back on the park," New Zealand head coach Gary Stead said. "Since the injury in June we've certainly taken a cautious approach to managing his return with regular monitoring by our medical staff which has included scans.
"While Kyle's not feeling any pain, the evidence is pretty clear he has a stress-fracture and so he'll return to Christchurch today and have a CT scan on Friday before we decide on the next steps."
Jamieson has made an outstanding start to his Test career with 72 wickets at 19.45 from 16 Tests.
The 33-year-old, who has 78 Test caps and taken 317 wickets at 27.49, missed the two-Test series in Pakistan and had been playing in the ILT20 for MI Emirates. He is now back at home in Mount Maunganui, just a 20-minute drive from the Bay Oval.
"We have spoken to Trent Boult recently and it has been decided since he gave up his contract that we will give priority to the locally contracted players and we have done that on this occasion," confirmed Stead.
"It does not mean we have ruled Trent out from anything in the future. There will be ongoing discussion and we're not sure what the landscape of the cricket world will look like in six months. It might change again."
Kuggeleijn's inclusion is likely to prove controversial, especially if selected in the XI for Thursday's day-night opener. He was tried and found not guilty of rape in February 2017, following a trial at Hamilton District Court.
He made his international debut during a tour of Ireland in May the same year, playing two ODIs, and the Northern Districts allrounder has since played 18 T20is. The first three of those came in New Zealand at the start of 2019 and prompted protests in the stands, ranging from #MeToo signs to others promoting sexual consent.
Stead defended the decision to pick Kuggeleijn, who averages 32.52 with the ball and 27.72 with the bat. "That's not my job, I guess, to do that," he responded when asked of the moral issues around the matter.
"I get given the players I can choose from and we have gone with a resilient character, from a bowling point of view, and he is a guy when you lose two key bowlers, you look around and ask who are the guys who can a job for us internationally and he is one who can.
"It is a rebuilding stage for us and you are tested with your depth when you lose two players on the eve of the Test match. Scott and Jacob are both resilient and offer something different. I would be surprised if one of them does not debut in this Test match."
New Zealand's preparations for the first Test have also been hit by the impact of Cyclone Gabrielle causing delays to some players arriving.
Tom Blundell, who recently welcomed his second child will also link up with the side later today, along with Henry Nicholls who had his original flight from Christchurch on Monday cancelled.