The suicide attack was the deadliest in the country's capital since newly-elected President Abdrabuh Mansur Hadi pledged to oust al-Qaeda militants from Yemen's mostly lawless and restive southern and eastern provinces.
Medics, speaking on condition of anonymity, said the casualties were being treated in seven hospitals across Sanaa. All the dead and injured were soldiers, they added.
There was no immediate claim of responsibility for the massive blast which according to witnesses echoed loudly across the city, causing panic among residents.
The unidentified bomber detonated his explosives as soldiers from the government's central security forces, commanded by a nephew of former president Ali Abdullah Saleh, rehearsed for an army parade to mark the 22nd anniversary of the unification of north and south Yemen, according to the military official.
Yemen's defence minister, Mohammed Nasser Ahmed, was present at the time of the explosion but escaped unharmed, the official added.
Witnesses said human remains were scattered across the site of the blast at Sanaa's Sabeen Square, where the Yemeni government often holds large military parades.
An AFP correspondent said dozens of ambulances rushed to evacuate the dead and wounded, as security forces cordoned off the area. The attack is Sanaa's most deadly since Hadi took power in February with a pledge to fight al-Qaeda's growing presence in the county.