Following the Hurricanes final game of the season, Smith required treatment on his left eye to repair a detached retina.
Hurricanes' doctor Ian Murphy said the two procedures went well and Smith was recovering at home, but the centre is expected to be out of training for six weeks.
That timeframe would see Smith sit out the All Blacks two matches against Australia in Sydney and Auckland to open the forthcoming four-nations competition, with the trip across the Tasman coming first on August 18.
Depending on whether Smith can recover early and resume training within the projected six weeks, the 30-year-old may be able to return for the All Blacks first match against Argentina on September 8.
Together with Sonny Bill Williams' unavailability following his decision to leave New Zealand rugby, Smith's absence leaves the All Blacks light on experience in midfield for the first rounds of the inaugural Championship.
