Báez came through Argentina's youth structures, representing the Pumas Under 19 team in 2008 and the Under 20 side a year later at the 2009 IRB Junior World Championship. He later went on to turn out for the Argentina Jaguars and was a member of the Pampas XV team that competed in the 2012 and 2013 Vodacom Cup competitions in South Africa, as well as their tour of Australia in 2014.[1]
He debuted for Los Pumas in May 2011 against Chile and capped his debut with a try in a comfortable victory for his side.[1]
In August 2014, he was named to the squad for the 2014 Rugby Championship[5] and made his first championship appearance as a substitute in a 9-28 loss to New Zealand on 6 September 2014.[6]
Báez is signed to play for Jaguares until 2017.[citation needed]