Cuadrado made his senior international debut in 2010, and has since earned 100 caps. He was part of the Colombian squads which took part at five editions of the Copa América (2011, 2015, 2016, 2019 and 2021), reaching the quarter-finals on three occasions, and contributing to their third-place finishes in 2016 and 2021; Cuadrado also represented his nation at two editions of the FIFA World Cup, in 2014 and 2018.