The flight was transporting the Brazilian side Chapecoense to Medellin airport when it disappeared off radar.
The jet is believed to have been carrying 72 passengers and nine crew, the country's civil aviation board confirmed.
A video shared on Twitter claimed to show the moment the plane disappeared from view on flight radar.
It is thought to have come down in Cerro Gordo in the municipality of La Union, according to Mi Oriente.
Colombian news website Noticias Caracol tweeted what is purported to be the first pictures of the wreckage.
At least 10 people have been injured and are being evacuated from the scene, the commander of La Union fire department said, according to the website.
Brazil's Chapecoense players pose for pictures Chapecoense are thought to have been heading to the final of the South American football championship.
Earlier in the day, the Chapocoense football team’s official Facebook page posted a video of the players waiting to board the flight at Viru Viru International Airport in the city of Santa Cruz de la Sierra, Bolivia.
The club also posted a picture of the team after boarding the flight.
