Regional criminal investigations chief Gideon Kibunja said today's dawn attack occurred at Lokichogio Mixed Secondary School near the countries' border.
Kibunja says a key suspect is a senior at the school who was suspended last week after he was found fighting and had vowed to take revenge.
The incident comes a month after a high school girl was charged with murdering nine of her colleagues in a fire at a Nairobi boarding school.
Kenya's border areas are littered with firearms from neighboring countries that have experienced war.