Reports say there are six survivors. The plane reported electrical problems.
The chartered aircraft, flying from Bolivia, was carrying members of the Chapecoense football team, airport officials said.
The team was due to play in the final of the Copa Sudamericana, against Medellin team Atletico Nacional.
The first leg of the final of the cup, South America's second most important club competition, was scheduled for Wednesday, but has now been suspended.
The South American Football Confederation (Conmebol) said it was suspending "all activities".
The team, from the southern city of Chapeco, was promoted to Brazil's first division in 2014 and reached the final last week after a victory against Argentina's San Lorenzo.
Reports say the British Aerospace 146 short-haul plane, operated by Bolivian charter airline Lamia and carrying 72 passengers and nine crew, crashed in Cerro Gordo in the municipality of La Union shortly before midnight local time (05:00 GMT).
据相关报道称,这架英国生产的Aerospace 146短程支线客机，由玻利维亚航空公司经营，机上有72名乘客及9名机组人员，于当地时间（格林尼治时间5点）在拉乌尼翁Cerro Gordo山区坠毁。
Medellin's Mayor Federico Gutierrez described it as "a tragedy of huge proportions".
Poor weather has meant that the crash site, in a mountainous area, is only accessible by land.
However, there was no fire on impact, which has given rescuers hope that more survivors may be found.
CONMEBOL said in a statement that its president, Alejandro Dominguez, was on his way to Medellin.
"The CONMEBOL family greatly regrets what happened. All activities of the confederation are suspended until further notice," it said.