Alonso missed several games at the end of the season for Real Madrid with back problems.
Del Bosque released his final 23-man squad on the Spanish federation website. He had announced a 26-man squad earlier in the week with plans to drop three players after the Spanish league concluded on Saturday.
Spain plays its first match at the June 15-30 tournament on June 16 against Uruguay in Recife.
Spain has won the past two European Championship titles and will look to retain its World Cup title at the 2014 tournament in Brazil.
The 31-year-old Alonso has formed part of Spain's midfield alongside Sergio Busquets and Xavi Hernandez during its winning run.
His absence may mean that Del Bosque will play a more attack-oriented formation and include another playmaker in his starting 11. Players who may come into the team include Santi Cazorla, Juan Mata, and David Silva.
Spain leaves for the United States on Tuesday to play friendlies against Haiti and Ireland to warm up for the tournament.
Defenders: Ignacio Monreal (Arsenal), Jordi Alba (Barcelona), Raul Albiol (Real Madrid), Gerard Pique (Barcelona), Sergio Ramos (Real Madrid), Cesar Azpilicueta (Chelsea), Alvaro Arbeloa (Real Madrid).
Midfielders: Andres Iniesta (Barcelona), Santi Cazorla (Arsenal), Sergio Busquets (Barcelona), Xavi Hernandez (Barcelona), Juan Mata (Chelsea), David Silva (Manchester City), Cesc Fabregas (Barcelona), Jesus Navas (Sevilla), Javier Martinez (Bayern Munich).