The plane crashed in Sanaa's northern neighbourhood of Al-Hassaba, according to an AFP photographer who saw three charred bodies lying on the ground at the crash site.
The airport source said the Antonov came down while trying to land at an air base near Sanaa's main airport.
"The military aircraft, which was on a training mission, tried to make an emergency landing after its engine failed but crashed at Al-Hassaba," the source told AFP.
A resident said three explosions occurred as the plane crashed, followed by plumes of smoke.
Firefighters and ambulances raced to the site, while a helicopter flew overhead, according to residents.