Bobby Gould, the Wales coach, had gambled on Williams recovering from an Achilles injury in time to play in their final Group Seven match on Saturday.
Gould said: "We wanted to give him every chance of making it. He came out with us to Brussels after having treatment morning, noon and night. But he trained in the morning and it clearly wasn't going to stand up to any real match action."
His plans are in crisis, as he has already lost Manchester City's Kit Symons with a knee injury. Queen's Park Rangers' Karl Ready and Watford's Robert Page are the only recognised centre-backs in the party.