Enzo posted a video to social media of Argentina's players singing a song aimed at their World Cup rivals France, taking aim at the make-up of the Les Bleus squad.
The Argentines sung how French players are "from Angola" or have a "Nigerian" mother and a "Cameroonian" father.
In reaction, Chelsea defender Wesley Fofana posted to X: "Football in 2024: uninhibited racism".
It then emerged that Fofana, Axel Disasi and Malo Gusto had all unfollowed Enzo on Instagram. Chelsea are now investigating the situation.
Later in the evening, Enzo posted an apology, stating: "I want to apologise for a video posted on my Instagram channel during the national team celebrations.
"The song includes highly offensive language and there is absolutely no excuse for these words. I stand against discrimination in all forms and apologise for getting caught up in the euphoria of our Copa America celebrations.
"That video, that moment, those words, do not reflect my beliefs or my character. I am truly sorry."