A security official said that the blast took place on Saturday after the explosive device which was planted close to a police checkpoint in the north of the capital went off as the policemen opened the bag to check its contents.
Two policemen were killed immediately by the blast which also injured two others. One of the wounded lost his life later.
No group has yet claimed responsibility for the attack. However, police have launched an investigation to find those behind the deadly assault.
Saturday’s explosion came after a period of calm in Sana’a. The Arabian Peninsula country’s politicians are currently participating in a national dialogue which seeks to lay the ground for a new constitution and planned February 2014 general elections.
In July 2012, a large bomb explosion targeting a police academy in Sana’a left least 25 people dead. Many others were also injured in the bombing at the entrance to the police academy.
In May 2012, at least 100 Yemeni troops were killed and more than 300 others injured after a bomb attack was carried out during a parade rehearsal in the capital.