The shooting occurred at dawn at Lokichogio Mixed Secondary School near the countries' border, Rift Valley regional criminal investigations Chief Gideon Kibunja said, AP reported.
A key suspect is a senior at the school who was suspended last week after he was found fighting and vowed to take revenge, Kibunja said.
The gunmen were looking for the school's principal and the student involved in the fight but couldn't find them, so they shot other students out of frustration, he said.
The shooting 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, including South Sudan and Somalia. High schools have experienced a wave of violent incidents in the past two years.