Davies ruptured his anterior cruciate ligament playing for his French club Clermont Auvergne against Montpellier on Saturday.
The Welsh Rugby Union said the 27-year-old will undergo surgery in the next few days and it is estimated Davies, who has won 48 caps for Wales, will be out of action for six to seven months.
The news is a significant setback for Wales, who face Australia, England, Fiji and Uruguay in their World Cup pool.
Davies was a damaging midfield ball-runner for the British and Irish Lions in their series win over the Wallabies in 2013 alongside fellow Welshman Jamie Roberts.
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