Coach Ralf Rangnick announced the squad of 29 players, taking into account a wave of recent and longer-term injuries.
Alaba, who played in two of Austria's previous Euros appearances in 2016 and 2020, picked up a major knee injury last December.
"It is a great shame of course that he isn't available to us as a player. Over the last weeks, I've have had close exchanges with David. He stressed he wanted very much to still be with us," Rangnick said.
"Therefore, I am very happy to say this will be possible after a good discussion with his club Real Madrid."
Midfielder Xaver Schlager will miss the tournament after damaging his left knee at the start of May, as will first-choice goalkeeper Alexander Schlager who also picked up a knee injury.
Austria face France, the Netherlands, and Poland in Group D at the Euros and play friendlies against Serbia on June 4th and Switzerland on June 8th.
