The incident occurred before Yemen's warring factions are to meet Sunday for UN-sponsored talks in Geneva in their first bid to break a deadlock after more than two months of Saudi-led air strikes.
The coalition led by Riyadh denied claims that it had carried out an air strike in Sanaa, suggesting instead that a rebel munitions cache may have exploded.
Residents of the quarter said a pre-dawn strike was the first direct hit there since the launch of the campaign against Iranian-backed Huthi rebels in late March.
"We saw the flashing light of the missile launched from a plane. We expected it to explode, but it did not... We felt the impact of the missile when it hit the ground," said resident Ahmed al-Ameri.
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Sanaa's old city has been inhabited for more than 2,500 years and was a major centre for the propagation of Islam, boasting more than 100 mosques, 14 public baths and more than 6,000 houses built before the 11th century.
UNESCO director general Irina Bokova said she was "profoundly distressed by the loss of human lives as well as by the damage inflicted on one of the world's oldest jewels of Islamic urban landscape."
She said she was "shocked by the images of these magnificent many-storeyed tower-houses and serene gardens reduced to rubble.
"The historic value and memories enshrined in these sites have been irreparably damaged or destroyed.
"This destruction will only exacerbate the humanitarian situation and I reiterate my call to all parties to respect and protect cultural heritage in Yemen," she said.
"I never imagined that this site could one day become a target; even if there were enemy (positions) in the area, it should never be a target for air strikes," he told AFP.
The upper storeys of houses rising above ground floors constructed of stone are built of rammed earth and burnt brick, with each building decorated with geometric patterns of fired bricks and white gypsum, inspired by traditional Islamic art.