Ponga, who received clearance earlier this year to switch his allegiance to New Zealand, scored two tries as his side fell to a 24-22 defeat to Australia on the opening night of the tournament.
Newcastle captain Ponga is viewed as critical to the Kiwis' hopes of claiming their first World Cup since 2008.
But coach Stacey Jones, whose side will face the Cook Islands in Christchurch next week before wrapping up their group stages matches against Fiji, said: "He couldn't catch a ball or anything like that. He was in a bit of discomfort."
Ponga was replaced by Keano Kini as he trudged off late in the match after playing through pain for the final 20 minutes.
"He's going to go and get the scans done and we'll see where it goes from there," Jones said.
"He's obviously disappointed, but there's a bit of upbeat about him too. He really wants to still be involved."
Ponga will head for further assessment on Friday ahead of New Zealand's return home.
If his tournament is over, the Kiwis will 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 if he is ruled out of 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."
