Lt Gen Vo Van Tuan, army deputy chief of staff, said the Huey chopper disappeared from radar about eight minutes after taking off from an air base in Ho Chi Minh City.
It's unclear what caused the chopper to go down, but the crash site was later discovered on a farm on the city's outskirts.
Tuan said the aircraft had originally belonged to American forces, but it was seized by communist forces after the war ended in 1975.
In July, a Russian-made helicopter on a training mission crashed near Hanoi, killing 20 people on board. One soldier survived with severe burns.