The gunmen stormed a room where secondary school students were taking an exam and exchanged fire with police officers guarding the campus before fleeing, they said.
"Students scampered for safety when the gunmen stormed the school and fired shots," a senior police officer from Wajir told AFP.
Six policemen were guarding the examination centre at the time, regional governor Mohamud Saleh said.
It was not immediately clear if the shooting was linked to the Al-Qaeda-linked Shabaab group, which regularly carries out attacks in Kenya, including a massacre at Garissa University in April 2015 in which 148 people were killed.
Saleh did not immediately comment on who was behind the attack, saying that an investigation was underway and that officials had "intensified security in the area".
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