Boult suffered a leg injury during the first Test in Dunedin which ended in a draw.
The left-arm pacer had left the field on Day Four of the Test match after bowling just 15 overs in South Africa's second innings. He was supposed to return on the final day which was eventually washed out.
Tim Southee, who was left out of the first Test to allow the Black Caps to accommodate two spinners, will replace Boult although the final XI will not be named until the morning.
"Injuries are part and parcel of cricket," ESPNcricinfo quoted Southee as saying.
"He has had a big workload with five one-dayers and a big four days in the Test match in Dunedin. Trent being one of the fittest guys in the side does everything he possibly can to keep himself fit, so it's unfortunate that it has come but I am sure he will be right come Hamilton."
The hosts have also lost Ross Taylor with a calf injury. Neil Brown will be replacing the veteran batsman and will make debut at No. 5.
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