Sabella was undergoing treatment for a heart condition at a hospital in Buenos Aires but gave up the ghost on Tuesday.
Sabella was in charge when Argentina lost the 2014 World Cup final 1-0 to Germany in Brazil.
He represented the likes of Boca Juniors, Sheffield United and Leeds United during his days as a player and led Estudiantes to win the 2009 Copa Libertadores as a manager.
"The AFA's Liga Profesional de Futbol family deeply regrets the passing of Alejandro Sabella, and is with all his loved ones at this sad time," the Argentine top flight's Twitter account confirmed on Tuesday as it paid its respects to the late coach.
"Rest in peace, Professor."
Barcelona superstar Lionel Messi, who was made captain during Sabella’s time as Albiceleste manager said on Instagram: "It was a pleasure to share so much with you."
"Alejandro was a great person, aside from being a model professional who shaped my career and helped me learn much from him.
"We enjoyed together some of my favourite footballing memories during qualification for the World Cup and in the World Cup itself. My condolences to all his family and friends."
Leeds tweeted: "The thoughts of everyone at #LUFC are with the friends and family of former midfielder Alejandro Sabella, who has sadly passed away. RIP Alex."
