Police say five people survived the crash but the rest of those on board died.
The chartered aircraft, flying from Brazil via Bolivia, was carrying members of the Chapecoense team.
The team was due to play in the final of the Copa Sudamericana, against Medellin team Atletico National.
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 match was seen as the biggest in the history of the relatively small club, which entered Brazil’s top division for the first time in 2014.
The South American Football Confederation (Conmebol) said it was suspending “all activities”.
Chapecoense issued a brief statement saying: “May God be with our athletes, officials, journalists and other guests travelling with our delegation.”
It said it would refrain from any further statements until it had assessed the extent of the crash.
Later the team’s vice-president, Ivan Tozzo, told cable channel SporTV: “There are a lot of people crying in our city. We could never imagine this. Chapecoense is the biggest reason for joy here.”
One of the survivors was confirmed as Chapecoense defender Alan Ruschel.
Reports suggest that at least two other footballers – goalkeepers Jackson Follman and Marcos Danilo – may have survived.
Originally six survivors were reported, but police later said one of those rescued had died.