Reports from Brazil say Danilo Feliciano de Moraes, Cafu's eldest son, complained of feeling unwell and was rushed to the Albert Einstein Hospital where he later died.
Several prominent football clubs have taken to social media to express their condolences to Cafu, 49, who represented his country a record 142 times over a 16-year career.
Sao Paulo - - Cafu's boyhood club - - wrote on Twitter: "Sao Paulo Futebol Clube deeply regrets the death of Danilo, son of Cafu. The club sympathises and wishes the tricolor idol, family and friends a lot of strength."
AC Milan also expressed its support for Cafu, who ran out 119 times for the Rossoneri, winning six titles including the 2007 Champions League.
"It's with a sad heart that we offer our deepest condolences to his family at this saddest of times," the Italian giant tweeted.
Inter Milan, Roma, Real Madrid and European football's governing body UEFA have also tweeted their condolences.
The news of Danilo's passing was confirmed by Cafu's long-time friend and Brazilian teammate Paulo Sergio, according the Brazilian outlet Globo Esporte.
Cafu is widely regarded as one of the game's best ever right-backs. He lifted 20 trophies with five different clubs. In addition his World Cup triumphs in 1994 and 2002, Cafu won two Copa Americas -- in 1997 and 1999 -- and the 1997 Confederations Cup. He is working with FIFA as an ambassador for the 2022 World Cup in Qatar.