The Inter star scored for the Nerazzurri on Sunday as they completed a famous comeback to beat Lazio 3-2 and squeeze into the Champions League ahead of the Rome side.
But despite finishing the season as Serie A top scorer on 29 goals, Icardi has been overlooked by Argentina coach Jorge Sampaoli.
Sampaoli takes just two specialist centre-forwards to Russia – recovering Manchester City star Sergio Aguero and Juventus’ Gonzalo Higuain.
The forward line-up is completed by captain Lionel Messi, Juve’s Paulo Dybala and 22-year-old Boca Juniors winger Cristian Pavon.
Elsewhere, Manchester United reserve Sergio Romero prepares for his third World Cup campaign after making the squad alongside fellow goalkeepers Willy Caballero and Franco Armani, drafted in after impressing for Atletico Nacional and River Plate in recent years.
There is also a call-up for Marcos Rojo, who managed just nine Premier League appearances for United in a season ravaged by injury.
In total just eight members of the Albiceleste squad that made the World Cup final in 2014 are called up for Russia.
Messi, Aguero, Higuain, Romero, Rojo, Javier Mascherano, Lucas Biglia and Angel Di Maria are the survivors, while the likes of Giovani Lo Celso, Pavon, Maxi Meza and Nicolas Tagliafico are among a host of players with less than 10 caps.
Argentina will take on Iceland, Croatia and Nigeria in the group phase, after coming through a tortuous qualifying campaign on the final day thanks to a famous hat-trick from Lionel Messi to down Ecuador.
Argentina’s World Cup squad:
Goalkeepers: Sergio Romero (Manchester United), Willy Caballero (Manchester City), Franco Armani (River Plate).
Defenders: Gabriel Mercado (Sevilla), Cristian Ansaldi (Torino), Nicolas Otamendi (Man City), Federico Fazio (Roma), Marcos Rojo (Man United), Nicolas Tagliafico (Ajax), Marcos Acuna (Sporting), Eduardo Salvio (Benfica).
Midfielders: Javier Mascherano (Hebei), Lucas Biglia (Milan), Ever Banega (Sevilla), Giovani Lo Celso (PSG), Manuel Lanzini (West Ham), Angel Di Maria (PSG), Maxi Meza (Independiente).
Forwards: Lionel Messi (Barcelona), Paulo Dybala (Juventus), Sergio Aguero (Man City), Gonzalo Higuain (Juventus), Cristian Pavon (Boca Juniors).