Seven policemen and three gunmen were killed, according to the interior ministry and security officials.
Another two policemen and two gunmen were wounded, and one of the attackers was captured, the ministry said.
The two-pronged attack began when an explosives-laden vehicle exploded at the facility's eastern entrance shortly after sunset, breeching a hole in the prison fence, security officials said.
At the same time, gunmen attacked guards at the main entrance, creating a diversion that allowed some of the prisoners to escape through the hole in the fence.
Residents said earlier that an explosion and heavy gunfire rang out near the jail, in the capital's north, where officials say around 5,000 prisoners are held, before security reinforcements were dispatched to the area.
In October, security forces foiled an attempt by some 300 Al-Qaeda inmates to escape after they mutinied in another Sanaa prison.
A number of guards and inmates were wounded but none killed .
Nasser al-Wuhayshi, chief of Al-Qaeda in the Arabian Peninsula -- seen by the United States as the network's deadliest franchise -- vowed in August to free imprisoned members of his network.
The AQAP detainees escaped through a 44-metre tunnel they dug between their cell and a nearby mosque.
Today's assault was the second major one in the capital in a little over two months.
In early December, a suicide bomber and several gunmen attacked the defence ministry in a brazen operation in broad daylight, killing at least 52 people and wounding another 167.
Today's operation came as Saudi Arabia's interior ministry announced that Yemen has handed over 29 Saudis wanted for suspected links to Al-Qaeda.
Nine others were on trial in the kingdom when they fled.
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