The device was planted near a police checkpoint in the north of the capital and detonated as the policemen opened the bag to check its contents, the official added.
The blast killed two of the policemen immediately and seriously wounded two others, one of whom died later.
A manhunt has been launched for those behind the attack, the official added.
Today's deadly blast came after a period of relative calm in the Yemeni capital.
The impoverished Arabian Peninsula country has been hit by violence attributed to Al-Qaeda militants, southern separatists and a Shiite rebellion in the north.