The 26-year-old had already been ruled out of the early rounds of the Super 14 as part of the All Blacks' conditioning programmes.
Collins will be able to resume aerobic exercise after one week and is expected to take part in contact training in approximately six weeks.
All Blacks doctor Deb Robinson said: "Jerry played with persistent pain through much of last year.
"We hoped that a period of rest would solve the problem, but the symptoms have returned now that he is back in training.
"He could carry on at less than 100%, but we've decided to address this now. It's a minor surgery and he'll be able to resume conditioning work after a week."