The United Nations said on Saturday that at least 60 people were killed in the attacks. Witnesses interviewed by Reuters described blasts hitting the centre, which was reduced to rubble, images show.
The Saudi-led coalition battling the Houthis has said the facility in Saada province was not included on a no-target list agreed with UN agencies. The coalition accused the Houthi forces of spreading unspecified misinformation about the attack.
Fighting has escalated in recent weeks, with more air strikes on what the Saudi-led coalition says are Houthi military targets. The Iran-aligned Houthi movement has stepped up missile and drone attacks on the United Arab Emirates and cross-border launches on neighbouring Saudi Arabia.
In Saada, a northern Houthi stronghold, survivors of the attack on the holding facility were still in hospital on Sunday.
Inmate Muhammad al-Khulaidi suffered a broken leg and burns. He said he managed to pull himself from the rubble of a cell, while some of his cellmates were killed.
"I was trying to free my leg from under the pillar and the warplane continued to bombard us," he told Reuters.
"I tried, I tried, and I removed the debris from under my leg, and I got out. I could not help my friends because my leg was broken," he said.
The United Nations has urged de-escalation in the nearly seven-year-old war in which more than 100,000 people have been killed and 4 million displaced. Millions of Yemenis are on the brink of famine.
The coalition intervened in Yemen in March 2015 after the Houthis ousted the internationally recognised government from power in the capital, Sanaa. The group says it is fighting a corrupt system and foreign aggression.