Gustavo Vargas could face a manslaughter charge over the deaths which included nearly all of Brazil's Chapecoense football team.
Bolivian prosecutors are also questioning along a mechanic and a secretary who worked for LaMia airline.
Police raided the airline's offices as well as those of the agency that oversees air traffic in Bolivia.
Officials are also investigating whether LaMia, which only received permission to fly earlier this year, was favoured by Vargas's son, Gustavo Vargas Villegas, who headed the office responsible for licensing aircraft in Bolivia's civil aviation agency.
Prosecutors from Brazil, Bolivia and Colombia are combining efforts to determine the cause of the November 28 crash.
They are also probing how the airline, despite its questionable history, amassed an impressive list of clients from among South America's top football clubs, was allowed to operate.
Some 19 members of Brazil's Chapecoense football team were killed in the disaster.
They were travelling to the opening match in the Copa Sudamericana tournament's finals.
One of the six survivors of the crash said he had been reassured by the airline before take-off that the plane would make a refuelling stop in the Bolivian town of Cobija, as it had on previous flights north.
"I don't know if it was a fuel problem - the investigation will determine that," Erwin Tumiri said.
"But every time we flew we went first to Cobija and returned the same way to refuel. On this occasion they said we'd do the same."
Meanwhile, an employee in Bolivia's aviation agency turned up in Brazil on Tuesday seeking asylum.
In a document widely circulating in Bolivian media, the worker, Celia Castedo, appears to have pointed out a number of irregularities in the aircraft's flight plan, including not having enough fuel, to LaMia's dispatcher, who was killed in the crash.
The authenticity of the document could not be immediately verified.
In Bolivia, a senior government official said Ms Castedo, who was among officials suspended following the crash, was potentially evading justice and should be immediately deported.
"What she has done is very serious," minister Carlos Romero told reporters, denying that she faced any persecution in Bolivia. "It's a way of escaping the judicial system."