Boult pulled up lame during South Africa's second innings in the drawn first Test in Dunedin to be the second senior player to be sidelined after Ross Taylor suffered a calf tear.
Neither side had finalised their line up on Wednesday for what should be a seam-friendly Basin Reserve wicket, but South African captain Faf du Plessis said the absence of Boult and Taylor would hurt New Zealand.
"If you lose two key players like that you definitely feel you're a little bit light," he said.
"For a new (batsman) coming in it's important for us to put pressure on him and not make him feel comfortable. From a bowling perspective Boult is a huge loss."
With the first Test drawn, Wellington is effectively the start of a two-Test series which du Plessis said heightened the need to get a result.
"When it comes to a two-match series you have to be a little bit more street smart because it can go both ways," he said.
"You go 1-0 down in the series there's no coming back from that so it's getting yourself in a position where you can try and make sure you win."
Although the team's have not been announced, Boult's long-time new-ball partner Tim Southee, who was dropped for the Dunedin Test, confirmed he was back in the side.
"I'll come in for Boulty, a straight swap for Trent who will unfortunately miss this one," Southee said, adding the balance of the side was still being debated despite the green wicket.
- Broom debut -
"There's a couple of question marks round a couple of players but I can confirm I come in for Trent and Neil Broom comes in for Rosco (Taylor). But they'll finalise the side tomorrow."
It will be Broom's Test debut but he has played 30 one-dayers including three in the recent series against South Africa where he had scores of two, two and a duck.
Seven Test seamer Matt Henry is the frontrunner to replace Boult and if the wicket dictates one spinner, New Zealand may overlook Mitchell Santner in favour of Jeetan Patel who bore the brunt of the workload in Dunedin.
Also in Patel's favour was having claimed Quinton de Kock's wicket in his past four innings, although du Plessis said his middle-order batsman did not consider himself Patel's bunny.
"Quinton doesn't over-analyse things too much. He relies on instinct so yes, Jeetan has got the best of him this series but Quinton will always find a way."
South Africa were also weighing up whether to change their line-up with du Plessis saying the playing XI would be decided by the state of the pitch on Thursday morning.
"I don't expect too many changes. We're looking at possibly, maybe, one but highly unlikely," he said.