"The plane was carrying 21 people and it crashed during a parachute training exercise, killing 16 and injuring five others," Lieutenant General Vo Van Tuan, army deputy commander, told AFP.
The dead and injured were all military personnel, he added.
"According to our preliminary investigation, the accident was due to technical problems. The weather was good and I can say that there was no act of sabotage," he added.
The Russian-made Mi-171 chopper came down in the early morning in the Thach That district, a sparsely-populated rural suburb in the west of the city, a military source told AFP on condition of anonymity.
It appeared to run into difficulties before crashing into the ground and bursting into flames, an eyewitness told AFP.
"I heard an aircraft making a strange noise... I ran outside and the aircraft exploded, there was a huge blaze then a plume of smoke," said one middle-aged local resident, speaking on condition of anonymity.
"The aircraft was flying low, it hit the ground and exploded at the same time," she said, adding it had looked like the helicopter was struggling to stay airborne before it crash-landed.
"It seemed like the pilot wanted to divert the plane from hitting the local market and houses, so it ran into that field," she said, gesturing towards the cordoned-off crash site.
The official Thanh Nien newspaper reported the helicopter smashed through the fence of one local property before bursting into flames.
"I heard someone shouting for help... there was another explosion and a lot of black smoke. Local residents rushed to help," the female resident told AFP.
Police and firefighters cordoned off the area, according to an AFP reporter at the scene.
Scores of people gathered near the local hospital and morgue.
Some locals had joined early rescue efforts but declined comment, saying they did not want to offend local authorities.
At the morgue, which had been blocked off by police and military officials, at least five ambulances were heading to Hanoi with military escorts carrying the remains of the victims.
State media said the injured had been transferred to hospitals in the centre of Hanoi.
In 2008 five Vietnamese military pilots were killed when their twin-engine light transport aircraft crashed on the outskirts of Hanoi.
The Soviet-designed Antonov An-26 turboprop crashed into a rice field south of the capital during a morning training flight.