Smith broke both his tibia and fibula in a tackle during the build-up to Lome Fa'atau's try in the sixth minute of the match.
The 24-year-old is to undergo surgery to insert a titanium rod into the bone of his right leg.
Smith's injury follows the one to regular midfield partner Tana Umaga, who missed Saturday's match with an Achilles and calf injury forcing coach Colin Cooper to bring Ma'a Nonu in from the wing to centre.
Nonu is likely to get an extended run in the midfield now.
Cooper admitted that Smith's injury was a cruel blow for the player and the Hurricanes.
"Conrad is a huge loss to our side and the entire squad really feels for him," said Cooper. "Our thoughts are with him at present and in terms of the Hurricanes, we lose his qualities as an excellent decision maker and a key organiser of our backline.
"You can't easily replace a player of his class, but we know he will bounce back strong once his rehab work is done."
Smith is hoping to return to action for Wellington in this year's new Air New Zealand Cup competition in October.