The incident happened when the Standard Eight pupil was playing with the gun, which belongs to his father, who is a police reservist.
The boy accidentally pulled the trigger, killing his friend on the spot.
Confirming the incident, Mutuati OCPD Cornelius Sing'oei said it appeared the shooting was not intentional.
"The boys wanted to learn more about how the gun operates," Mr Sing'oei told the Nation by phone.
Police said the two boys were pupils at Katherwa Primary School.
The incident comes barely three weeks after a 16 year old boy shot dead his 12 year old colleague in neighbouring Isiolo County while herding cattle.
Following the Isiolo incident, County Commissioner Wanyama Musiambo said it was illegal for parents to allow children to herd animals using firearms.
