Gustavo Vargas, a retired air force general, has been detained as part of an investigation into the crash.
The plane, operated by the tiny LaMia airline, was taking the team to Colombia when it ran out of fuel.
A Bolivian official says she warned the pilot of the problem before departure.
The official, Celia Castedo, has now sought asylum in Brazil, saying she suffered threats and abuse.
Chapecoense were travelling to the city of Medellin to play the first leg of the Sudamericana Cup final against Atletico Nacional.