The 32-year-old forward will undergo surgery to rectify an ongoing back problem, ruling him out of the rest of the Super Rugby season with the Christchurch-based Crusaders.
"He has tried every non-invasive trick you could do to get right and it just hasn't come off, so he'll be in the operating theatre by the end of the week," Crusaders head coach Rob Penney said.
"He's got his head around it now - a pretty special trip to South Africa that he's going to miss and some other bits and pieces. But ultimately, he's just got to get himself right."
Barrett was appointed New Zealand's 81st Test captain when former Crusaders coach Scott Robertson became the national head coach in 2024. He has led the All Blacks in 11 Tests.
Robertson was removed as All Blacks coach in January and Dave Rennie, a former Wallabies head coach, has taken over.
Rennie has yet to select a captain, but it has seemed increasingly unlikely he would retain Barrett.
Barrett's brother, Jordie Barrett, is among the leading candidates to take over the captaincy, along with back-rower Ardie Savea and hooker Codie Taylor.
New Zealand play their first Tests in the new Nations Championship against France in Christchurch on July 4, Italy in Wellington on July 11, and Ireland in Auckland on July 18.
They then undertake a tour to South Africa and the US that will include four Tests against the World Cup champion Springboks.
The tour also involves provincial matches against the Stormers, Sharks, Bulls and Lions.
