Coach Vicente del Bosque has also overlooked Manchester United midfielder Juan Mata and Atletico Madrid's former Liverpool forward Fernando Torres.
Holders Spain are in Group D, along with Croatia, the Czech Republic and Turkey as they chase a third successive European Championship title.
Brazil-born Costa has scored one goal in 10 games since switching allegiance.
The 27-year-old netted 16 goals in 41 appearances for Chelsea this season, but missed their final two games with a persistent hamstring injury.
"We didn't want to have too many players with doubts regarding their physical condition," said Del Bosque, who led Spain to the 2010 World Cup and Euro 2012 titles.
Mata, 28, featured in both of Spain's friendly matches in March, but misses out after a season where he scored nine goals and provided eight assists for his club.
Torres, 31, has scored seven goals in his past 11 games, leading to speculation he might be recalled for the first time since Spain's embarrassing exit at the group at the 2014 World Cup.
Bayern Munich defender Javi Martinez and Arsenal midfielder Santi Cazorla are other notable omissions, while coach Del Bosque has included Athletic Bilbao's 35-year-old striker Aritz Aduriz.
There were also call-ups for uncapped pair Saul Niguez of Atletico Madrid and Real Madrid's Lucas Vazquez.
The Premier League-based players are: Manchester United goalkeeper David de Gea, Chelsea trio Pedro, Cesar Azpilicueta and Cesc Fabregas and Manchester City playmaker David Silva.
Goalkeepers: Iker Casillas (Porto), David de Gea (Manchester United), Sergio Rico (Sevilla)
Defenders: Jordi Alba, Gerard Pique, Marc Bartra (all Barcelona), Sergio Ramos, Dani Carvajal (Real Madrid), Cesar Azpilicueta (Chelsea), Juanfran (Atletico Madrid)
Midfielders: Sergio Busquets, Andres Iniesta (both Barcelona), David Silva (Manchester City), Mikel San Jose (Athletic Bilbao), Koke, Saul Niguez (both Atletico Madrid), Cesc Fabregas (Chelsea), Thiago Alcantara (Bayern Munich), Isco (Real Madrid), Bruno Soriano (Villarreal)
Forwards: Pedro Rodriguez (Chelsea), Alvaro Morata (Juventus), Aritz Aduriz (Athletic Bilbao), Nolito (Celta Vigo), Lucas Vazquez (Real Madrid)
Chelsea striker Diego Costa has been left out of Spain's provisional squad for Euro 2016.