Although Argentina were the hosts for the 2014 Quidditch World Cup in the Patagonian desert, the host team had not, unfortunately, qualified to play in the tournament. The Argentinian Minister for Magic, Valentina Vázquez, is noted as having attended (Pm).
Although Argentina hosted a Quidditch World Cup and should have played in 1877 (and restaged 1878) tournament, there are not any wizard sports listed on its Wikipedia page (Wikipedia).
From the Web
Writing by J.K. Rowling on Pottermore:
- History of the Quidditch World Cup
- 2014 Quidditch World Cup reports
- 2014 Quidditch World Cup final
- The Daily Prophet
Pottermore enhanced reading experience: Quidditch World Cup
Screenshots of the original Daily Prophet coverage of the 2014 Quidditch World Cup on Pottermore: Imgur web archive
Harry Potter Wiki: Argentinian National Quidditch Team