Officials said that six people survived the crash near Medellin.
The British Aerospace 146 short-haul plane, operated by a charter airline named LaMia, declared an emergency at 10pm local time on Monday because of an electrical failure, aviation authorities said.
The aircraft, which had departed from Santa Cruz, Bolivia, was transporting the Chapecoense team to Medellin’s Jose Maria Cordova airport.
The team, from southern Brazil and which had started its journey in Sao Paulo, was scheduled to play on Wednesday in the first of a two-game Copa Sudamericana final against Atletico Nacional of Medellin.
It was not immediately clear if the team switched planes in Bolivia or just made a stopover with the same plane.
“What was supposed to be a celebration has turned into a tragedy,” Medellin Mayor Federico Gutierrez said from the search and rescue command centre.
The club said in a brief statement on its Facebook page that “may God accompany our athletes, officials, journalists and other guests travelling with our delegation”.
Brazil as well as South America’s football federation extended its condolences to the entire Chapecoense community and said its president, Luis Dominguez, was on his way to Medellin.
All football activities were suspended until further notice, the organization said in a statement.
Elkin Ospina, mayor of La Ceja - near where the crash took place, said rescuers working through the night had been heartened after pulling three passengers alive from the wreckage.
Authorities and rescuers were immediately activated but an air force helicopter had to turn back because of low visibility.
Heavy rainfall complicated the night-time search, and authorities urged journalists to stay off the roads so ambulances and other rescuers could reach the site.
Images broadcast on local television showed three male passengers arriving to a local hospital in ambulances on stretchers and covered in blankets connected to an IV. All were apparently alive and one of them was reportedly a Chapecoense defender named Alan Ruschel.
The plane was carrying 72 passengers and nine crew members, aviation authorities said in a statement.
Local radio said the same aircraft transported Argentina’s national squad for a match earlier this month in Brazil, and previously had transported Venezuela’s national team.
A video published on the team’s Facebook page showed the team readying for the flight earlier on Monday in Sao Paulo’s Guarulhos international airport.
The team, from the small city of Chapeco, was in the middle of a fairy tale season. It joined Brazil’s first division in 2014 for the first time since the 1970s and made it last week to the Copa Sudamericana finals - the equivalent of the Uefa Europa League tournament - after defeating two of Argentina’s fiercest squads, San Lorenzo and Independiente, as well as Colombia’s Junior.
The team is so modest that its 22,000-seat arena was ruled by tournament organisers too small to host the final match, which was instead moved to a stadium 300 miles to the north in the city of Curitiba.
“Chapecoense was the biggest source of happiness in the town,” the club’s vice-president, Ivan Tozzo, told Brazil’s SporTV. “Many in the town are crying.”