The policemen were killed when the bomb attached to their vehicle exploded in a central district of Kabul on Saturday, police spokesman Ferdaws Faramarz told reporters, aljazeera.com reported.
A civilian was also wounded in the blast, he said.
Two security personnel were wounded in another similar bomb attack targeting a second police vehicle in a western district of Kabul, Faramarz said.
He said a third bomb also exploded in the city but caused no casualties.
In recent months, Kabul and several other provinces of Afghanistan have been rocked by deadly violence, including bombings, rocket attacks and targeted killings.
Several of these attacks, especially in Kabul, have been claimed by the Daesh terrorist group.
Journalists, politicians and rights activists have increasingly been targeted as violence surges in the country.
This comes as ‘peace talks’ continue between the Taliban and the Afghan government.
The Taliban and the Afghan government are taking a break until January 5, after reaching a preliminary agreement this month.
The preliminary deal is the first written agreement between the two warring sides since the US-led invasion of Afghanistan in 2001.
The intra-Afghan negotiations had been set to take place in March, but were repeatedly delayed over a prisoner exchange made as part of a deal between the Taliban and the US.
Under that deal, signed in February, the Taliban agreed to halt their attacks on international forces in return for the US military's phased withdrawal from Afghanistan and the prisoner exchange with Kabul.
Afghanistan has been gripped by insecurity since the US and its allies invaded the country as part of Washington's so-called war on terror in 2001. Many parts of the country remain plagued by militancy despite the presence of foreign troops.