The Aston Villa star was also found guilty of "violating principles of fairplay" in two separate episodes.
Martinez was found to have violated FIFA's code of conduct when holding a replica of the Copa America trophy to his groin after the World Cup qualifier win over Chile on September 5th.
It is not the first time Martinez has performed such an action having also done it with the Golden Glove trophy for best goalkeeper after Argentina beat France on penalties in the 2022 World Cup final.
FIFA also sanctioned him for hitting a TV cameraman's camera with his gloves after their 2-1 defeat by Colombia on September 10th.
The AFA expressed their dissatisfaction with the FIFA ruling.
"It should be noted that the Argentine Football Association expresses its absolute disagreement with the decision taken by the FIFA disciplinary committee," they said in a statement.
As a result of the decision Martinez - also a key member of the Argentina side that won the Copa America in July, as well as the 2021 edition - will miss the World Cup qualifiers against Venezuela on October 10th and Bolivia on October 15th.
Argentina are top of the South American qualifying table with 18 points after eight matches. Colombia are just two points behind.