The policeman was killed near the 13th district of the city, said police spokesman Ferdaws Faramarz.
No individual or armed group claimed responsibility for the attack.
The police spokesman said investigations had begun.
In another incident, two terrorist attacks were foiled in the 19th district of the capital.
A remote-controlled explosive device and a keg bomb was found in Ali Khel area of Kabul city, the Ministry of Defense said.
According to the source, the bomb was found and detonated away from residential areas.
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