In a statement, Brigadier Abdul-Razaq al-Mu'aid al-Mu'aid said that one of the members of the cell was arrested at the site of the attack, while the rest were apprehended with the help of information provided by the latter.
They were arrested at the Immigration and Passports Authority while attempting to get documents to flee abroad, al-Mu'aid said. The perpetrators belonged to the Al Qaeda militant group.
He also affirmed that the owner of the small pick-up truck, which was detonated, was identified and that security services were searching for him.
On Wednesday, at least 37 people were killed and dozens of others wounded when a car bomb exploded outside the police academy.
It is the most deadly attack in Sanaa since Oct 9, 2014, when an Al Qaeda suicide bomber blew himself up at a gathering of the Shiite Houthi group, killing at least 47 people.
On June 11, 2012, an Al Qaeda suicide bomber attacked this police academy, killing at least 21 people. Security situation in the impoverished Arab country has worsened since the Shiite militia took control of Sanaa by force September 21, 2014.
The Al Qaeda in the Arabian Peninsula (AQAP), known locally as Ansar al-Sharia, has conducted several bomb attacks against the Houthi group, government and army, killing scores of people.
On Monday, an explosive device went off at an office of the Shiite Houthi group in western Sanaa, wounding two people and damaging nearby houses.