The Sukhoi crashed into "Al-Asbahi residential district in southern Sanaa," the official told AFP.
The official did not provide further details.
The accident is the second of its kind in the capital this year after 12 people died in February when another military aircraft ploughed into a building in a residential area.
That plane had also been identified as a Sukhoi SU-22 attack aircraft, and had been on a training mission.
An air base is located near the Sanaa international airport, just 15 kilometres north of the capital.
In November, a Yemeni air force Antonov M26 crashed during a training mission in a northern district of Sanaa, killing all 10 on board.
A fighter jet crashed on takeoff on a routine training mission in the south in October, killing the pilot and injuring another crew member, after what the defence ministry described as a "technical failure."
And in October 2011, four people were killed when an Antonov crashed on landing at Al-Anad air base in southern Yemen.
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