Barrett made his debut for the All Blacks against Samoa early this year and started at fullback in the final test against the British and Irish Lions.
The 20-year-old suffered the injury in the Hurricanes Super Rugby semi-final loss to the Lions in Johannesburg and will require surgery, which means he won't be back in 2017.
"It's a pretty clear cut injury. The ligament has come off and it's basic reattachment," said assistant coach Ian Foster.
"Pretty frustrating for him. He's had an amazing six months. There's probably no silver lining in a significant injury but ...when he reflects on his year - he's done massively well in the Hurricanes environment and come in (to the All Blacks) and had a couple of test matches...and done himself proud."
He has been replaced in the squad by Crusaders fullback David Havili, who impressed in their title-winning season.
Foster said Havili's promotion was well earned, after a strong season with Super Rugby champions the Crusaders.
"While he's a utility, he stepped into that fullback role and done a great job."
Foster said while Havili has spent a lot time in the midfield at Super Rugby level, he had developed well at fullback with a kicking game, running the ball back well and improving defensively.
"He brings a nice all round skill set that we have been interested for a while, but been unable to find a place (for him)."