He is not expected to play again until next summer, meaning he will miss New Zealand's two-test series against Australia when it starts later this month.
"The last few days have been some of my most challenging but I am hugely grateful for the support I've received from my partner, family, teammates, support staff and medical professionals," said Jamieson.
"I know injuries are part of life as a cricketer and at my age I am hopeful I still have many more playing days ahead of me."
Jamieson had complained of back pain after New Zealand's win over South Africa in their first test earlier this month and did not play in the second test.
The Black Caps won in Hamiltoin by seven wickets on Friday to complete a series victory.
Jamieson had surgery last year to treat an injury in the same location, but NZC say he will only require "rest and rehabilitation to give the injury the best chance to heal".
