Police were notified on Wednesday morning that a man had opened fire at the school in the town of Sanski Most with an automatic rifle, police spokesman Adnan Beganovic said.
The shooter killed the school dean, the secretary and a teacher, he said.
"He tried to commit suicide and was gravely injured," Beganovic said, adding the suspect was transferred for emergency treatment in the nearby town of Banja Luka.
An investigation was under way, he said.
The school had not yet reopened from the summer holidays so no children were involved.
N1 TV, citing witnesses, said a janitor who had a history of disagreements with the management and was under disciplinary proceedings, sought out specific people and shot them.Â
Reuters could not immeditely verify that report.
Mass shootings are comparatively rare in the Western Balkans, which is awash with weapons that remained in private hands from wars in the 1990s.
In July, a war veteran in neighbouring Croatia shot five people including his mother in a nursing home and wounded six others.
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