Williams and Amos failed to recover from the knee and shoulder injuries respectively which they suffered during the second half of their side’s pivotal 28-25 victory over Pool A rivals England at Twickenham on Saturday.
Gloucester’s vastly experienced and versatile back James Hook as well as New Zealand-born Gareth Anscombe have been added to the Welsh squad as replacements.
“It’s a blow to lose another two players but the resilience, the character we showed at Twickenham on Saturday, I’m sure you’ll see in abundance over the next four or five weeks,” said attack coach Rob Howley.
Coach Warren Gatland has now lost five members of his original World Cup squad following the enforced withdrawals of key trio Leigh Halfpenny, Rhys Webb and Cory Allen.
Wales will be in touching distance of the quarter-finals should they beat Fiji at the Millennium Stadium on Thursday. Fiji wing Nemani Nadolo, meanwhile, will miss the clash after being slapped with a one-match ban for a dangerous tackle against Australia.