Barrios, who scored two goals at last year's Copa America in Chile, was included in Paraguay's provisional squad, having featured in 2018 FIFA World Cup qualifiers against Brazil and Ecuador in March.
However, there was no room for the 31 year-old Palmeiras attacker in the final 23-man squad ahead of the century edition of the tournament, which will kick-off in the United States on 3 June.
Victor Caceres, Jonathan Santana, Osvaldo Martinez and Raul Bobadilla were also among 16 players culled, with Roque Santa Cruz and Paulo da Silva to lead the way for Paraguay next month.
Drawn in Group A, two-time champion Paraguay opens its campaign against Costa Rica on 4 June.
The Paraguayans clash with Colombia three days later before tackling host nation the USA on 11 June.
Goalkeepers: Diego Barreto (Olimpia), Antony Silva (Cerro Porteno), Justo Villar (Colo Colo)
Defenders: Pablo Aguilar (America), Fabian Balbuena (Corinthians), Paulo Da Silva (Toluca), Gustavo Gomez (Lanus), Blas Riveros (Olimpia), Miguel Samudio (America), Bruno Valdez (Cerro Porteno)
Midfielders: Miguel Almiron (Cerro Porteno), Nestor Ortigoza (San Lorenzo), Celso Ortiz (AZ Alkmaar), Robert Piris Da Motta (Olimpia), Rodrigo Rojas (Cerro Porteno), Oscar Romero (Racing Club)
Forwards: Edgar Benitez (Queretaro), Jorge Benitez (Cruz Azul), Derlis Gonzalez (Dynamo Kiev), Nelson Haedo Valdez (Seattle Sounders), Juan Iturbe (AFC Bournemouth), Dario Lezcano (Ingolstadt), Roque Santa Cruz (Malaga)