North Queensland Cowboys star Thurston, named as the NRL's joint Player of the Year with Jarryd Hayne of the Parramatta Eels, helped the Kangaroos to World Cup glory in 2013 and has also won two Four Nations titles in his international career.
But the 31-year-old will be unavailable for this year's tournament, which starts on October 25 as the world champions host New Zealand at Suncorp Stadium in Brisbane.
Although the injury will not require surgery, Thurston has been advised to forego his international commitments and withdraw from the squad.
"It was a really difficult decision to have to make but in the end, the doctor really took it out of my hands when I saw him yesterday," Thurston told the Cowboys' official website.
"You never want to miss playing rep footy, and I'm very proud of my record in that area, but this time there's no other option.
"I'd like to wish the Kangaroos all the best for the Four Nations.
"I'll definitely be watching every match they play and cheering them on."