Ponga failed to finish his long-awaited Test debut for the Kiwis, departing in the 70th minute of the 24-22 loss after suffering the injury earlier in the second half.
Receiving clearance earlier this year to switch his allegiance to New Zealand, Ponga delivered a stand-out performance at CommBank Stadium as his side fell to Australia in the Thursday night thriller.
The Newcastle skipper scored two tries while running 253 metres from 16 runs, making three line breaks and five tackle breaks.
He has been booked in for surgery after breaking his radius in his left arm but Kiwis team doctor Greg Macleod sounded hopeful about the prospect of Ponga playing again through the tournament.
"We wish Kalyn all the best with his surgery today," Macleod said in a statement.
"We'll see how that goes but for now he will remain in camp."
The 28-year-old is viewed as critical to the New Zealand's hopes of claiming their first World Cup since 2008.
Coach Stacey Jones, whose side will face the Cook Islands in Christchurch next week before wrapping up their group stages matches against Fiji, said Ponga had played through pain.
"He couldn't catch a ball or anything like that. He was in a bit of discomfort," Jones said.
Ponga was replaced by Keano Kini as he trudged off late in the match and was seen on the sidelines with his arm in a sling.
"He's obviously disappointed, but there's a bit of upbeat about him too. He really wants to still be involved," Jones said.
If New Zealand decide Ponga's tournament is over, the Kiwis have the option to ask for clearance to add an additional player to their squad.
"He's a tough guy and obviously has a lot of pride in the black and white jersey, and he doesn't want to let his teammates down," said Kiwis captain James Fisher-Harris.
"I thought he did an outstanding job, he's a freakish player, but he's also one of those tough players. We're feeling for him right now, but fingers crossed it's not too bad."
Jones said Kini would likely replace Ponga in next week's pool match.
The Kiwis' narrow loss to Australia was one that will burn Jones for a while.
Two of the Kangaroos' five tries were the result of interceptions and another two were from kicks.
The Kiwis dominated territory but lacked the polish to make Australia pay for their mistakes.
"Unfortunately, we were on the losing side, but we will learn from it and we will get better, and we will make some adjustments," Jones said.
"You go in that changing room and everyone's down, they're hurting.
"But you just bounce back and you get back into it. We know these boys, they work hard, they're professional, we'll be okay."
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