The incident took place in the vicinity of the 8th police district of the city in Chaman Hazoori area o the city.
Deputy spokesman for the Ministry of Interior Nusrat Rahimi said the target of the explosion was a group of the protesters and as a result at least three people were wounded.
He said the explosion was triggered by a magnetic improvised explosive device as a number of people had participated in a sit-in protest.
However, another security official said at least one person was killed and nine others were wounded in the explosion.
In the meantime, the Kabul Police Department spokesman Basir Mujahid said at least one person was killed and thirteen others were wounded in the blast.
No individual or group has so far claimed responsibility behind the incident.
This comes as the anti-government armed militant and terrorist groups have been attempting to carry out deadly terrorist attacks in the key provinces and cities of the country including capital Kabul.
More than thirty people were killed and around fifty others were wounded after a suicide bomber detonated his explosives near the Sakhi shrine in Kabul city on Wednesday.