Paris Saint Germain winger Angel Di Maria was also included but there was no place for striker Gonzalo Higuain, who is on loan at Chelsea from Juventus.
"These are the best players in an important time for the national team," said Scaloni ahead of the tournament hosted by Brazil, which begins on June 14.
Argentina will play in Group B alongside Colombia, Paraguay and guests Qatar, the 2022 World Cup hosts and current Asian champions.
Messi, who only returned to the Argentina squad in March after an eight-month absence following the World Cup in Russia, will turn 32 during the competition.
Di Maria, like Messi, made his post-World Cup return in March ahead of friendlies against Venezuela and Morocco, but Manchester City's Aguero had not been called up since Argentina's 4-3 last 16 defeat to eventual champions France in Russia.
Another high-profile omission was Inter Milan forward Mauro Icardi, who has been left out of the Italian team's line-up for the last two months over a dispute regarding a contract renewal.
"Keeping everyone happy is difficult," admitted Scaloni, who said he'd had "doubts right until the end" over the final squad make-up.
Argentina have not won the Copa America, or any major international tournament, since 1993, losing in the final in four of the last five editions of the continental showpiece.
Squad:
Goalkeepers: Agustin Marchesin (America Mexico/MEX), Franco Armani (River Plate), Esteban Andrada (Boca Juniors)
Defenders: German Pezzela (Fiorentina/ITA), Juan Foyth (Tottenham Hotspur/ENG), Nicolas Otamendi (Manchester City/ENG), Nicolas Tagliafico (Ajax/NED), Marcos Acuna (Sporting Lisbon/POR), Renzo Saravia (Racing Club), Ramiro Funes Mori (Villarreal/ESP), Milton Casco (River Plate)
Midfielders: Leandro Paredes, Angel Di Maria (both Paris Saint-Germain/FRA), Guido Rodriguez (America Mexico/MEX), Giovani Lo Celso (Real Betis/ESP), Roberto Pereyra (Watford/ENG), Rodrigo De Paul (Udinese/ITA), Exequiel Palacios (River Plate)
Forwards: Lionel Messi (Barcelona/ESP), Sergio Aguero (Manchester City/ENG), Paulo Dybala (Juventus/ITA), Lautaro Martinez (Inter Milan/ITA), Matias Suarez (River Plate).