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The Stoke City forward, 32, limped off after 64 minutes of Monday's 1-1 Group E draw with Sweden in Paris.
Walters has not trained since and his absence for the Belgium game was confirmed on Friday.
West Brom midfielder James McClean, Walters' replacement against Sweden, is expected to start in Bordeaux.
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Belgium - ranked second in the world - lost 2-0 to Italy in their opening game.
Italy, who beat Sweden 1-0 on Friday to seal their progress into the last 16, take on the Republic in Lille next Wednesday.
"He thinks he is going to be able to make the Italian game," O'Neill said of Walters on Wednesday.
Wes Hoolahan's opener for the Republic against Sweden at the Stade de France was cancelled out by a Ciaran Clark own goal.
"If that performance doesn't lift you, nothing will," said O'Neill.
"We will have to show the same attitude again, go and compete and be strong on the ball."
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Republic of Ireland striker Jonathan Walters has been ruled out of Saturday's Euro 2016 clash against Belgium because of an Achilles injury.