The fire affected a dormitory which accommodates up to 60 boys.
Kiambu County Police Commander James Mugera said the fire started at about 1 am on Monday as most students were sleeping.
He said investigation into the incident have been launched in order to know the cause of the fire.
Police want to establish if the incident was the work of arsonists.
Those injured were admitted to Limuru Sub County Hospital.
A team of detectives were at the school recording statements from management and students.
Stephjoy Boys High School is a private school with more than 400 students.