They said the man, who was not identified, used a Kalashnikov assault rifle and was later shot and killed by security forces in the south-central province of Kerman.
They said the cause of the shooting, in a remote rural village, was a family dispute. They did not elaborate.
Mass killings are rare in Iran, where hunting rifles are the only weapons people are allowed to possess. Two years ago, a dismissed employee of a state institution in western Iran shot and killed three people and injured five before killing himself.