Martinez will miss next month's World Cup qualifiers against Venezuela and Bolivia after being punished by FIFA for two incidents that took place in the last international window.
The first incident took place after a 3-0 home win over Chile in what was Argentina's first match since winning the 2024 Copa America.
Martinez held a replica Copa America trophy against his crotch in a repeat of his infamous celebration with the Golden Glove award after the 2022 World Cup final.
Martinez receives two match ban
The Aston Villa goalkeeper has also been punished for a second indecent which took place following the 2-1 away defeat to Colombia on September 10.
Martinez struck a local television camera with his gloves after Argentina fell to their first defeat since losing to Uruguay in November 2023.
A statement from the Argentine Football Association read: "Despite the defense made by the player and the Argentine Football Association, the Disciplinary Commission of the governing body of World Football made the following decision:
"Martinez is declared responsible for his offensive behaviour and his violation of the principles of fair play (art. 13 CDF).
"It should be noted that the Argentine Football Association expresses its absolute disagreement with the decision taken by the FIFA disciplinary committee."
Who will replace Martinez?
Marseille's Geronimo Rulli and PSV Eindhoven's Walter Benitez were called up his Martinez's understudies for the games against Chile and Colombia.
Argentina boss Lionel Scaloni will now have to decide whether to start Rulli or Benitez for October's World Cup qualifiers against Venezuela and Chile.
Rulli last featured for his country in September 2022, while Benitez's sole international appearance took place in a friendly against Chile earlier this year.
Scaloni will also need to call a third goalkeeper, with Atletico Madrid's Juan Musso among those who could be named in the squad.