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 channal SportTV: "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 Danilo - may have survived, as well as physiotherapist Rafael Gobbato.
The sports network Telemundo Deportes tweeted (in Spanish) that Ruschel was in shock but conscious and talking, and asked to keep his wedding ring and to see his family.
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.
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).
According to a Colombian airport press release, it had reported an electrical fault to the control tower.
Medellin's Mayor Federico Gutierrez described it as "a tragedy of huge proportions".
The Jose Maria Cordova de Rionegro airport, which serves Medellin, posted on its Twitter account: "Confirmed, the aircraft licence number CP2933 was carrying the team @ChapecoenseReal. Apparently there are survivors."
Poor weather meant that the crash site, in a mountainous area, was only accessible by land, and later Medellin airport tweeted (in Spanish) that the rescue operation had been suspended.
There was no fire on impact, which appears to have increased the chances of survivors being 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.
Chapecoense football team Founded in 1973.
Promoted to the Brazilian top division, Serie A, for the first time in the club's history in 2014. Currently ninth.
Were flying to play in the first leg of the final of the Copa Sudamericana - winner qualifies for Copa Libertadores, top continental competition in South America.
Were underdogs - facing current Cope Libertadores holders Atletico Nacional
Based in the Brazilian city of Chapeco in the state of Santa Catarina.
Brazil's 21st biggest club in terms of revenue at 46m reais ($13.5m/£10.9m)