There has been no let-up in the air campaign against the rebels that a Saudi-led coalition has been waging since March 2015 despite an appeal by UN chief Antonio Guterres on Sunday for a renewed push to end the "stupid war".
All of the casualties in the pre-dawn strikes on the camp in the capital Sanaa were prisoners, rebel television said.
An AFP photographer saw rebel fighters carrying away bodies from the rubble of heavily damaged buildings.
He said a first strike had damaged one wing of the jail prompting some of the prisoners to try to escape but it was then almost flattened by a second strike.
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Three further strikes damaged two other prison buildings and the perimeter wall, Aqel added.
On Sunday, Saudi-led strikes on a rebel training camp northwest of the capital killed at least 26 rebel fighters, security sources said.
On Friday, a strike on a rebel-controlled television station in Sanaa killed four guards.
The raids come with Yemen plunged deeper into turmoil by the killing of ex-president Ali Abdullah Saleh by the rebels after their uneasy alliance collapsed.
More than 8,750 people have been killed since the coalition intervened, most of them civilians, according to the World Health Organization.
On Monday, the UN humanitarian coordinator for Yemen, Jamie McGoldrick, warned: "8.4 million Yemenis are a step away from famine.
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