In addition, seven other policemen were injured. However, local security sources said civilians have also been injured, including a consulate staff member.
The siege ended after almost four hours.
The source said that the attack took place at about 9:00am local time in PD 3 in Jalalabad after a suicide bomber detonated his explosives at the Pakistan Consulate and opened the way for at least two attackers to enter.
A number of policemen killed were reportedly guarding the consulate at the time of the attack.
No group including the Taliban has claimed responsibility for the attack yet.
Meanwhile, the Ministry of Interior said in a statement that a "group of terrorists targeted a police vehicle near the Pakistan Consulate at 8:50am."
However, local officials say the attack was on the consulate itself.