"There are no survivors. Our embrace of solidarity to the families and the armed forces. It is a tragedy," President Rafael Correa said on Twitter (in Spanish).
Nineteen of the people on board were Ecuadoran soldiers travelling for a parachuting exercise.
The Israeli-built Arava plane crashed at 14:30 local time (19:30 GMT) in the eastern province of Pastaza.
The cause of the accident is unknown.
There were also two pilots and one mechanic on board, EFE news agency reported.
Defence Minister Ricardo Patino and rescue teams are travelling to the area.
An army plane with 22 people on board has crashed in Ecuador's Amazon region.