Rincon, 55, was hospitalized with severe injuries following an accident in the city of Cali on Monday.
The midfielder won 84 caps and scored 17 goals for Colombia, representing his country at successive World Cups in 1990, 1994, and 1998.
He started his playing career in Colombia with Santa Fe and American de Cali before moving to Europe, where he had spells at Italian sides Parma and Napoli, along with Spanish giants Real Madrid.
He spent two seasons at the Bernabeu and then returned to Latin America, going on to win a Club World Cup and two Brazilian league titles with Corinthians.
Colombia’s football federation termed Rincon’s death a “great loss,” while FIFA offered condolences to Rincon’s “loved ones, former teammates and fans from the clubs he played for.”
Real Madrid also issued a statement expressing “condolences and warmth to all of his family members, teammates, coaches, clubs and loved ones.”