"We will plan and support Toby's recovery, making sure it is the very best for him, in order to maximise his successful return to the game."
The 28-year-old has suffered a run of cruel luck with injuries, having not played a test for Wales since the 2018 Six Nations.
Faletau missed the internationals late last year with a broken arm. He then fractured the arm again in January, ruling him out of this year's Six Nations, where Wales went on to win the Grand Slam.
Despite his absence, Faletau was still expected to play a major role for Wales at the World Cup, having been one of their top performers at the past two tournaments.
According to Opta, Faletau made the most carries (49) and beat the most defenders (12) of any Wales player during the 2015 World Cup, in which they were knocked out by South Africa in the quarter-finals.
With Faletau now unavailable, Wales head coach Warren Gatland is likely to stick with the same back row trio who helped deliver a first Grand Slam in seven years, with flankers Josh Navidi and Justin Tipuric joined by Ross Moriarty at No 8.
Aaron Wainwright was frequently used by Wales in the Six Nations and therefore is also on track to be selected, leaving one more back-row place in Gatland's 31-man squad. Aaron Shingler, Dan Lydiate, Thomas Young and Ellis Jenkins, recovering from a serious knee injury, are all in contention.