Inter Milan's Martinez remained on the bench for the second leg of their Champions League round of 16 win over Feyenoord last week with muscle discomfort.
The 27-year-old returned to score in Inter's 2-0 Serie A win over Atalanta on Sunday, before joining Lionel Scaloni's squad, but he has now been ruled out with an injury in his left hamstring.
Martinez joins Argentina's growing list of absentees, including captain Lionel
Messi, sidelined with a muscle strain, along with Gonzalo Montiel, Giovani Lo Celso, and Paulo Dybala.
Argentina lead the CONMEBOL qualifying standings with 25 points after 12 games.
The World Cup and Copa América holders play at second-placed Uruguay on Friday before hosting fifth-placed Brazil four days later.