A police officer at the site said the three were aged up to 12 years-old.
Two more children were wounded in the blast after they knocked the munition against a rock in a residential area that was the scene of bitter fighting between rival Afghan factions in the 1990s, he said.
In a separate incident, a rocket-propelled grenade exploded after it was dropped by a policeman as his unit set off from Kabul on an opium poppy eradication mission north of the city, Zemarai Bashary, an interior ministry spokesman, said.
Landmines threat
One policeman was killed and at least eight were wounded, Ahmad Zia Aftali, the chief of the hospital where the injured were taken for treatment, said.
A policeman who witnessed the blast said more than 15 people were hurt in total.
Another police official, Sayed Ekramudin, said two civilians were killed and 13 others wounded in an explosion on Sunday at a refuse dump in the city's northern outskirts.
Ekramudin said a truck had hit a buried explosive.
Landmines and unexploded ordnance kill or maim several dozen people each month in Afghanistan, according to the United Nations.
There are millions of unexploded munitions and landmines across Afghanistan dating from three decades of war.