La Albiceleste will attempt to defend the trophy that they won in 2021 when they travel to the United States for next month's tournament.
The 2022 World Cup winners will begin their campaign against Canada on June 20, before they conclude the group stage with games against Chile and Peru.
In preparation for the tournament, Argentina will face Ecuador in Chicago on June 9 and Guatemala in Landover on June 13.
Argentina boss Lionel Scaloni has named a 29-man party to compete in those two friendlies before he whittles his squad down to 26 players for the Copa America.
Dybala left out of Copa America squad
Dybala will not be given a chance to impress in those warm-up games after being left out of Argentina's preliminary squad.
The playmaker has been in fine form for Roma this season, scoring 16 goals and providing 10 assists in 38 competitive appearances.
However, those performances have failed to convince Scaloni, who has also decided to leave out Walter Benitez, Juan Foyth, Marcos Senesi and Thiago Almada.
Unsurprisingly, Argentina's record appearance holder and goalscorer Lionel Messi has made the cut, leaving the Inter Miami forward on the verge of featuring at his 12th major international tournament.
Messi is joined in the squad by other established names such as Nicolas Otamendi, Rodrigo de Paul and Angel Di Maria.
Scaloni includes several Premier League names
Aston Villa goalkeeper Emiliano Martinez has been included and remains Argentina's first-choice goalkeeper after winning the Golden Glove Award at the 2022 World Cup.
Martinez is joined in the squad by eight Premier League players, including Liverpool's Alexis Mac Allister, Chelsea's Enzo Fernandez, Nottingham Forest's Gonzalo Montiel and Brighton & Hove Albion's Valentin Barco.
Manchester United will be represented by Lisandro Martinez and Alejandro Garnacho, while Tottenham Hotspur's Cristian Romero and Giovani Lo Celso have also been named in the 29-man squad.
There is also a spot for Manchester City forward Julian Alvarez, who recently claimed his second Premier League winners' medal.
Scaloni has until June 12 to confirm his 26-man squad for the tournament.
Argentina Copa America 2024 squad in full
Goalkeepers: Emiliano Martinez (Aston Villa), Franco Armani (River Plate), Geronimo Rulli (Ajax)
Defenders: Gonzalo Montiel (Nottingham Forest), Nahuel Molina (Atletico Madrid), Leonardo Balerdi (Marseille), Cristian Romero (Tottenham Hotspur), Nicolas Otamendi (Benfica), German Pezzella (Real Betis), Lucas Martinez Quarta (Fiorentina), Lisandro Martinez (Manchester United), Marcos Acuna (Sevilla), Nicolas Tagliafico (Lyon), Valentin Barco (Brighton)
Midfielders: Rodrigo De Paul (Atletico Madrid), Alexis Mac Allister (Liverpool), Enzo Fernandez (Chelsea), Leandro Paredes (Roma), Guido Rodriguez (Real Betis), Exequiel Palacios (Bayer Leverkusen), Giovani Lo Celso (Tottenham Hotspur), Valentin Carboni (Monza)
Forwards: Lionel Messi (Inter Miami), Angel Di Maria (Benfica) Lautaro Martinez (Inter Milan), Julian Alvarez (Manchester City), Nicolas Gonzalez (Fiorentina), Angel Correa (Atletico Madrid), Alejandro Garnacho (Manchester United)