"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."
However, Thurston said he would not require surgery on the injury.
Daly Cherry-Evans came off the bench in the Kangaroos' last test, a 30-18 win over the Kiwis, and is the most likely candidate to partner Cooper Cronk in Australia's halves.
NSW halfback Trent Hodkinson took a knee injury into Canterbury's grand final loss to South Sydney and is likely to undergo surgery, ruling him out.
That could open the way for Canterbury's Josh Reynolds to play alongside Cooper, or even Brisbane's Ben Hunt, or one of Sydney Roosters duo Mitchell Pearce or James Maloney, who have all been named in the train-on squad.
Either way Sheens will be forced to blood a number of test rookies over the coming weeks.
The long list of omissions has also brought the spotlight on to the issue of player burnout.
The Four Nations follows a 24-match season, a four-week finals series, the three-game State of Origin series and the Anzac test.
Sheens will name his squad next Tuesday.
Aussie squad absentees
Johnathan Thurston (shoulder), Billy Slater (shoulder), Darius Boyd (personal issues), Brett Morris (shoulder), Matt Scott (shoulder), Nate Myles (biceps), Paul Gallen (drugs ban), James Tamou (neck), Matt Gillett (shoulder), Justin Hodges (knee), Josh Dugan (thumb), Trent Merrin (shoulder), Will Hopoate (leg), Dave Taylor (neck), Andrew Fifita (arm).
