Argentina will meet rivals Brazil in Melbourne on June 9 before a clash with Singapore four days later.
Icardi, 24, who has made just one appearance for the Albiceleste, has scored 26 goals in 41 matches for Inter this season.
Lanzini, also 24, has 15 goals in 68 appearances for West Ham since his 2015 move from Al Jazira.
Argentina are currently fifth in the 10-team South America zone World Cup qualifying standings with four games remaining.
Only the first four teams at the end of the qualifying tournament will earn an automatic slot in Russia. The fifth-ranked side will advance to a playoff against the top nation from Oceania.
Sergio Romero (Manchester United), Nahuel Guzman (UANL Tigres), Geronimo Rulli (Real Sociedad)
Nicolas Otamendi (Manchester City), Emanuel Mammana (Olympique Lyonnais), Javier Mascherano (Barcelona), Gabriel Mercado (Sevilla)
Eduardo Salvio (Benfica), Lucas Biglia (Lazio), Guido Rodriguez (Tijuana), Leandro Paredes (AS Roma), Ever Banega (Inter Milan), Manuel Lanzini (West Ham United), Angel Di Maria (Paris Saint-Germain)