Medics said the toll, which included two children and three women and left another 22 injured, was expected to rise
Several hours after the crash rescue teams were still sifting through the rubble in search of any survivors in the Qadissiya area of homes and shops near Change Square, epicentre of the 2011 uprising that ousted president Ali Abdullah Saleh.
A military source identified the plane as a Russian-made Sukhoi SU-22 attack aircraft, but was unable to say what caused the crash that he said killed pilot Mohammed Shaker.
The defence ministry said the pilot was returning to his base after a training mission and had asked authorisation to land when suddenly the aircraft lost altitude and crashed. An investigation is underway.
"I saw the plane drop and we were afraid it would crash on Sanaa University, but the pilot crashed on nearby buildings," said Mohammed al-Sabri.
The aircraft hit one building on Rabat Avenue in eastern Sanaa, then smashed into another before finally crashing on top of a third, witnesses said.
An AFP correspondent said the building was badly damaged and that several ambulances rushed to the scene as helicopters hovered overhead.
A loud explosion shook the area when the crash occurred, witnesses said. Thick black smoke billowed over the district, where several cars were ablaze.
Panicked residents took to the streets, many screaming.
"We heard a loud explosion and we thought it was a mortar shell that landed on the neighbourhood," one of the residents, Taha al-Inad, told AFP.
An air base is located near the Sanaa international airport, just 15 kilometres (nine miles) north of the capital.
Tuesday's crash was the latest in a series of air accidents in the impoverished Arabian Peninsula country.
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.
Sanaa was gripped by violent clashes between rival military groups during the 2011 uprising to oust Saleh, who finally stepped down a year ago under a UN-backed power transition agreement brokered by the Gulf Cooperation Council.