The news was confirmed soon after coach Julen Lopetegui said he hoped the Chelsea striker still had a chance of playing in the match.
In a tweet, Spain said Costa would be replaced in the squad by Celta Vigo's Iago Aspas.
Costa, 28, scored one goal and set up another in Chelsea's 5-0 triumph over Everton on Saturday but has missed Spain's two opening training sessions in Madrid with muscle fatigue and a left groin bruise.
Earlier, Lopetegui had told Onda Cero: "We will see how he progresses. It's true that his recovery has not been as positive as we had expected.
"But we are hopeful that he will feel better tomorrow and we can take a small step forward thinking ahead of Saturday's game. We have to wait."
Brazil-born Costa had a slow start to his Spain career but has been in good form for Chelsea this season, scoring nine goals and setting up three more in 11 Premier League starts.
He has played in all four Spain games since Lopetegui replaced Vicente del Bosque at the helm of the national team in July and started three, scoring three goals.
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