Saleh's vehicle was struck by an RPG fire on Monday and he was later shot to death, raising questions about what happens next in the almost three-year war that has killed at least 10 000 people. The two camps had together been fighting pro-government forces backed by a Saudi-led military coalition that includes the UAE.
The assault and hostage-taking comes amid heightened tensions after forces loyal to former president Ali Abdullah Saleh severed ties with the Houthis, sparking days of gun battles and artillery fire in the capital.
A video circulating on social media showed fully-veiled women chanting "The people want the martyr's body".
The collapse of the alliance between Saleh and the rebels saw at least 100 people reported dead in fighting, accusations of betrayal and the former leader reaching out to the Saudi- led coalition.
It was not immediately clear if the rebels would allow Saleh's family to hold a funeral later in the day. "He got what he deserved", Ali Akbar Velayati, an aide to Iran's supreme leader, was quoted as saying by the semi-official Tasnim news agency. The coalition threw its support behind Saleh when he turned on the rebels, and may now back his son. The Arab League's general secretariat condemned the Iran-aligned Houthi movement which killed Saleh as a "terrorist organisation" and demanded that the global community view it as such.
The Houthis and Saleh's forces began fighting each other in Sanaa last week.
The war and blockade has plunged Yemen into a major humanitarian disaster, leaving 20 million people in need of aid.
The head of Iran's powerful Revolutionary Guard says a plot against Yemen's Shiite rebels was "nipped in the bud", apparently referring to the killing of former President Ali Abdullah Saleh.
But over the past year, the Houthis appear to have undermined Saleh, wooing away some of his commanders.
Worldwide aid groups warned today they were losing the ability to reach civilians in Sanaa.
Clashes in the Yemeni capital have killed at least 234 people and wounded 400 since December 1, the International Committee of the Red Cross said on Tuesday.
The casualty tolls provided by the ICRC are separate from those sustained in airstrikes by the Saudi-led coalition which is waging war on the rebels, known as Houthis.
Jamie McGoldrick, of United Nations aid agency OCHA, said civilians in Sanaa are "emerging from their houses after five days being locked down, basically prisoners", to seek safety, medical care, fresh water and other survival needs.