Williams, a tryscorer in last weekend's win over Scotland, strained his ankle in the 26-13 triumph at Murrayfield and had been rated as '50-50' to make Saturday's Millennium Stadium encounter by national coach Warren Gatland.
Gatland gave his match-winning wing until Friday afternoon to confirm his availability but Williams failed a fitness test and will therefore not be involved against Martin Johnson's men.
Scarlets wing Mark Jones come straight into the starting XV in place of Williams, despite not being originally named in the matchday 22.
Jones has not played for more than eight weeks after contracting appendicitis but Wales backs coach and former Lions tourist Rob Howley insists Jones will not let his country down.
"Mark steps in and we are comfortable with Mark," said Howley.
"Mark has never let us down when he's played for Wales and he was outstanding against Australia.
"He's proudly trained throughout the week. He's looking forward to that challenge."
Andy Powell was also subject to a fitness test alongside Williams but there was better news for the No8 who recovered sufficiently from a calf strain to take his place at the back of the Welsh pack.