The chartered aircraft, flying from Bolivia, crashed on its approach to the city of Medellin’s international airport.
The flight was carrying members of the Chapecoense football team, airport officials said.
Ambulances and rescuers were on their way to the crash site and it was possible there are survivors, the city’s mayor Federico Gutierrez said.
The plane crashed in a mountainous area outside the city shortly before midnight local time (5am GMT), according to reports.
"It's a tragedy of huge proportions," Mr Gutierrez told Blu Radio as he made his way to the site.
It is not clear what caused the crash of the aircraft, a British Aerospace 146 short-haul plane, but Colombia had been hit by heavy rains and thunderstorms in recent hours.
The plane was initially reported to be carrying 81 people on board, although it was not known if that figure included the crew.
The first division Chapecoense football team, from southern Brazil, were on their way to Colombia for a regional tournament final.
They were scheduled to play in the first of a two-game Copa Sudamericana final against Atletico Nacional of Medellin on Wednesday.
In a statement on its Facebook page, Chapecoense said: "May God accompany our athletes, officials, journalists and other guests traveling with our delegation."
The team said it would refrain from any further statements until it had fully evaluated the extent of the crash.
A video published on the team's Facebook page showed the team readying for the flight earlier Monday in Sao Paulo's Guarulhos international airport.
The team, from the small city of Chapeco, joined Brazil's first division in 2014 for the first time since the 1970s and made it to the Copa Sudamericana finals last week by defeating Argentina's legendary San Lorenzo squad.
