Otamendi scored his first goal for Argentina on 2 September 2011, in a 1–0 friendly win over Venezuela in Kolkata, after heading a corner taken by Lionel Messi. After being cut from the squad that later appeared at the 2014 World Cup, he was selected by coach Gerardo Martino for the 2015 Copa América, playing the entirety of all but one match as they lost to hosts Chile on a penalty shootout in the final; he was named in the Team of the Tournament.