The two teams had got the game underway but the referee stopped play after the tragedy, in which a fan fell from the grandstand.
River Plate, in a statement, have confirmed that the supporter "died on the spot", and the area needed to be cordoned off so that emergency services could tend to the deceased, named as Pablo Marcelo Serrano, a 53-year-old supporter.
In their statement, they also insist there was no violence leading to the tragic fall.
The club has confirmed that the stadium will be closed for 24 hours and have declared a day of mourning.
They said: ""The medical service immediately arrived at the area of
"The Sivori Alta grandstand was at 90% of its capacity. At the time of the fall, there was no intervention by third parties. It was also verified that there was no situation of violence in the stands or around it."
The statement added: "River Plate announce a day of mourning, with the flag at half mast; During the day on Sunday, the activities of the club will be reduced to the minimum and essential."
His nephew posted a tribute to his uncle on Twitter, writing: "I love you with my soul, uncle. Heaven has one more angel. RIP."