He scored 17 goals during his international career and was on the scoresheet against Argentina in a 5-0 World Cup qualifier victory in Buenos Aires in 1993.
A statement from the Colombian Football Federations read: "The Colombian Football Federation deeply regrets the death of Freddy Eusebio Rincón Valencia, and sends a message of support and encouragement to his family, friends and relatives at this difficult time.
"This constitutes a great loss for his family and friends, and it is also an unfortunate departure for our sport, where we will miss him and remember him with great affection, appreciation, respect and admiration.
"We send strength, support and our condolences to his family, hoping they can bear this sad and painful loss."
Fifa issued a statement to pay tribute to Rincon and honoured his memory by posting his memorable injury-time goal against West Germany at the 1990 World Cup, where Colombia needed to draw the game to avoid elimination from the group stages.
Rincon was played through by a pass from team-mate Carlos Valderrama, firing the ball through the legs of goalkeeper Bodo Illgner to spark wild celebrations among the South Americans.
"We join together with many in the world of football to remember Freddy Rincon," a Fifa statement read.
"Our sincere condolences go to his loved ones, former team-mates and fans from the clubs he played for, and of the Colombia national team who he represented at three World Cups. Rest in Peace."
