The Samoa international suffered the injury in the Raiders' defeat to Brisbane and the surgery puts him out of action for the rest of the campaign.
They're also without fellow forward Corey Horsburgh for the next four matches, with the lock losing at the NRL judiciary on Tuesday in his attempt to have a shoulder-charge ban overturned.
Horsburgh will only have the chance to play again this year if the Raiders reach the grand final.
It is a huge double blow for the Raiders ahead of a crucial final-round clash with Cronulla, where they may need victory to ensure finals football.
Joe Tapine, Papali'i's long-time front-row partner, said it takes a serious injury to keep the 31-year-old veteran down.
"I knew something was wrong because you never know when he's got an injury, he doesn't really say anything but he said he couldn't really lift his arm," Tapine said.
"It's a huge blow, my middle partner who I love playing with and such a leader in the middle.
"A lot of boys will have to step up and have to do a job for us, especially in the back end of the year."
Canberra named Emre Guler to start and picked potential debutant Hohepa Puru on the bench, the latter expected to join the starting lineup after Horsburgh's appeal failed.
Youngster Ata Mariota will play a bigger role and Pasami Saulo could also join the side from the reserves list, while Tapine said he'd told coach Ricky Stuart he could play more minutes in the front row.
"I'll probably still play No.10, I just said to 'Stick' I'll try and drag out some more minutes, I'm capable of doing it," he said.
"In the past we've just had the luxury of not having to drag out (minutes), so I'm happy to step up."
In a boost for Stuart and his Raiders, halfback Jamal Fogarty (eye) trained on Tuesday and is expected to line up against the Sharks.
Winger Albert Hopoate (ribs) could also come into calculations as the Raiders bid to maintain a winning record against Cronulla which stretches back to 2018.
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