The Real Madrid winger scored his side's key second goal in extra-time against city rivals Atletico Madrid in Lisbon last weekend, as the Spanish giants won the Champions League final 4-1 and lifted the European Cup for an unprecedented tenth time.
However, injury has now seen the former Tottenham Hotspur star withdraw from Wales manager Chris Coleman's squad that he takes to Amsterdam.
"Bale, who scored for Real in Saturday's Champions League final win against Atletico, has been troubled with a leg muscle injury for a few weeks.
"His place in the squad will be taken by Fulham's George Williams," the FAW added.
While the Netherlands are heading to the forthcoming 2014 FIFA World Cup™ finals in Brazil, Wales have not reached the tournament stages of a major international football competition since the 1958 World Cup in Sweden.