Smith suffered the injury in the Highlanders draw against the Chiefs in Dunedin at the weekend.
His injury raises concern in the All Black camp too with utility back Damian McKenzie already ruled out of the World Cup with a serious knee injury.
Highlanders assistant coach Glen Delaney says they're getting used to operating without key players.
"We've had guys dropping out throughout the year (through injury). We lost Aaron Smith for a bit, we had Liam (Squire) out for a bit and Waisake (Naholo's been out for a bit," said Delaney.
"It's just rugby...players get injured. We can't do anything about it. We'll support Ben and make sure the rehab is right and he's back and firing on all cylinders as soon as as he can.
"We'll miss him for sure as he's great to have around and he's a great leader on the field and we're very lucky that he and Luke (Whitelock) have been co-captaining so we don't lose all our leadership at once - we've got Luke out there and plenty of other guys to support him."
On a brighter note for the Dunedin based franchise, Delaney confirmed All Blacks loose foward Liam Squire and winger Naholo had returned to training and were available for selection.
Third in the New Zealand Conference with six rounds remaining until the post-season, the Highlanders need a victory over Argentina's in-form Jaguares at home on Saturday to keep in touch with the playoff positions.
Smith, who has won 76 All Blacks caps, is playing his final season with the Highlanders before moving to Pau in France so he might never play for the Dunedin-based side again if they fail to make the playoffs.
Delaney said All Blacks blindside flanker Squire and winger Waisake Naholo had returned to training and were available for selection.
Battling hip and knee problems, Squire has not played since facing Ireland for the All Blacks in November, while Naholo has been out for a month after suffering a knee ligament injury.
Delaney suggested both would be eased in gently if selected to face the Jaguares.
"(Squire's) full of energy and enthusiasm and doing all the right things and speaking well to the group," he said.
"He's just getting through day by day but the one thing we won't do with either of those guys is that they won't be back before we think they are ready.
"We'll look after them because it's important to us and obviously to some other teams as well."