Born in Granadero Baigorria, Monzón began his professional career with Boca Juniors in 2007 after being promoted out of the club's youth academy.

First, he failed to move to Ukrainian side Dnipro due to a congenital heart condition and a few days later a second transfer was cancelled, this time to Serie A team Udinese, admittedly by differences in payment method.

During his one and only season in Nice, he was a regular feature in the club's starting lineup, managing 34 league appearances, marked with 8 goals, a great performance for a left defender.

[10] On 9 January 2013, Monzón signed a 6-month loan deal with Brazilian national champions Fluminense in order to replace Thiago Carleto who returned to São Paulo.

[12] On 16 July 2013, Monzón officially signed for Calcio Catania in the Italian Serie A on a four-year contract[13] for €3.3 million, while a further €300,000 could be paid on performance-related bonuses.

[16] Monzón was a member of the Argentine squad for the 2008 Beijing Olympics, which also were figures like Lionel Messi, Sergio Agüero, Ángel Di María and Juan Román Riquelme.