Martinez earned his third Argentina cap in March during a 3-1 loss to Venezuela, starting alongside Lionel Messi, but wasn't called in by manager Lionel Scaloni.
The 25-year-old isn't off to a flying start in his Atlanta United career, though has turned in improved performances over recent weeks. The Copa America runs from June 14-July 7, meaning the club could have been without one of their stars for about six weeks, pending report date and how far the South American powerhouse progresses.
Atlanta are already without Ezequiel Barco, who is with Argentina at the U-20 World Cup. That tournament kicks off Thursday.