The Bath player was injured during Wales training and will need surgery.
The British and Irish Lion broke his arm twice last season and missed Wales’ Six Nations Grand Slam and has not played in a Test since March 2018.
A statement by the Welsh Rugby Union said: “The Wales squad and management would like to wish Taulupe the very best with his recovery.”
Faletau’s luckless run of injuries started in October 2018 when he fractured his right forearm while playing for Bath, which ruled him out of Wales’ autumn series clean sweep.
The 28-year-old made an impressive return for his club in their Champions Cup win over Wasps in January – but he then broke the same arm, and the injury denied him what would have been a second Grand Slam and a third Six Nations title of his career.
He returned to the Wales squad for their summer camp in Switzerland when he said he was hungry to play again after a frustrating time out of the game.
When fit, Faletau is ranked amongst the finest back-rows in world rugby and has played 72 times for Wales since making his debut against the Barbarians in 2011.
He has also made four Test appearances for the Lions across two tours, and scored a crucial try in the second Test win against New Zealand in 2017.
Dragons back-row Ross Moriarty filled in at number eight during Wales’ Six Nations Grand Slam campaign, but Faletau’s return was seen as a major boost in a department where Wales have some depth.
Scarlets’ Aaron Shingler also missed last season but has trained during the summer, while Cardiff Blues’ Josh Navidi can play in all three positions across the back row.
Wales play two Tests against England and two against Ireland before their World Cup starts against Georgia on 23 September.
Coach Warren Gatland will cut his provisional squad from 42 players down to a final 31-man party in early September.