Martinez recently received a two-match suspension by FIFA for two separate incidents that took place in the previous set of international fixtures.
The first incident saw Martinez repeat his infamous celebrations from the 2022 World Cup following a 3-0 qualifying win over Chile, which represented Argentina's first match since they won the 2024 Copa America.
The 32-year-old held a replica Copa America trophy against his crotch as Argentina celebrated their triumphant summer.
Five days later, Martinez struck a camera with his gloves after being approached by a camera operator following a 2-1 defeat against Colombia.
Martinez issues apology for Argentina suspension
After being punished for those two incidents, Martinez will now miss Argentina's next two World Cup qualifiers against Venezuela on October 10 and Bolivia on October 15.
The Aston Villa goalkeeper has now broken his silence on the ban, having taken to social media to apologise for his actions.
In a post on Instagram, Martinez wrote: "I accept the sanction from FIFA and I apologize if I offended anyone, the moment of celebration is to make many kids smile and not to disrespect anyone.
"I will support my friends on this FIFA date with the pain of not being able to be there.
"It was never my intention to disrespect anyone, nor did I understand that a gesture well received by people was offensive, but I will try not to offend anyone anymore and just focus on winning titles with Argentina and Aston Villa."
When will Martinez play for Argentina again?
Argentina boss Lionel Scaloni will likely pick either Walter Benitez or Geronimo Rulli to deputise in Martinez's absence.
However, the former Arsenal shot-stopper is expected to return to the starting lineup once he has completed his suspension.
As a result, Martinez should be in goal when Argentina travel to Paraguay for a World Cup qualifying clash on November 13.
La Albiceleste will then return home for a meeting with Peru on November 18, representing their final outing of the calendar year.
Argentina currently sit top of the CONMEBOL World Cup qualifying standings after winning six and losing two of their eight matches.