The 24-year-old trained on his own at Wales' Newport base on Monday afternoon but his fitness will not be risked as he recovers from a foot injury.
Bale, who has not played for Spurs in nearly a month, has been widely linked with a world record transfer to Real Madrid.
Bale was understood to be concerned at doing further damage to his foot with the move potentially on the horizon, and an FAW spokesman confirmed to Press Association Sport he will not be in Chris Coleman's matchday plans.
Tottenham manager Andre Villas-Boas had said last weekend he did not expect Bale to be fit for the north London club's Barclays Premier League opener against Crystal Palace on Sunday, but the winger travelled to south Wales to meet up with his international team-mates on Monday morning.
Despite being unavailable to play the Republic of Ireland, Spurs are happy for Bale to remain in camp with Wales where he will continue to train and will be in the stands at Cardiff City Stadium on Wednesday evening.
Bale is the third player that has been ruled out for Wales. Earlier on Monday Arsenal midfielder Aaron Ramsey and West Ham defender James Collins withdrew from the squad with ankle and knee injuries respectively.
Swansea full-back Jazz Richards and Brighton midfielder Andrew Crofts have been called up as replacements.