The giant prop will undergo surgery on Friday after he fell on his elbow during a drill at their Melbourne training ground on Wednesday morning.
In obvious pain, he was rushed for scans, which confirmed the worst.
The Storm have looked to the 20-year-old - at 200cm and 115kg one of the biggest players in the NRL - to steam-roll the tiring defence when he comes off the bench.
Christian Welch looms as the most likely to replace him for Saturday week's preliminary final at AAMI Park against Penrith or Canberra.
Storm football director Frank Ponissi said it was a blow for Asofa-Solomona and the team.
He earlier missed five weeks with a knee injury as well as being sidelined this season through two suspensions.
The injury could end his hopes of selection for the New Zealand team for the end-of-year Four Nations tournament.
"Nelson's injury is bitterly disappointing for him and the team, particularly with the impressive form he has shown this season," Ponissi said.
"While we are disappointed to lose Nelson, a feature of our team this season has been our depth and the resilience of the players to come into the side and play their role.
"We have no doubt whoever replaces Nelson, will come in and do just that."
While Asofa-Solomona is out, the Storm are confident hard-working lock Dale Finucane will overcome an ankle injury to play.
Finucane didn't take part in team training on Wednesday in Melbourne but the club believed he would be fit for the grand final qualifier.
Coach Craig Bellamy said this week was a balancing act in trying to maintain the team's momentum and giving his players a well-deserved rest.
"Sometimes you worry about missing that game in that it might dent your momentum a little bit, as we've been pretty good the last couple of games and we'd like to keep that going," Bellamy said.
While his heart is with his old playing club Canberra, Bellamy says he can't split the Raiders and Panthers.
"I've got a bit of a soft spot for Canberra as that's where I played but, having said that, the game could go either way.
"They're two really good teams in really good form and I'm sure it will be a good game."
