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.