The incident was "probably related to psychological problems of the soldier who suddenly started firing on his comrades," the statement said.
It took place on a shooting range, and could also have been the result of a gun misfiring, the statement added.
"The injured were transported to a medical centre and an investigation has been opened," it said.
Iran hits back at missile test criticism
State television reported a similar incident last month when a serviceman opened fire at a barracks in Abyek, around 40 kilometres northwest of Tehran, killing three and injuring six.
The gunman in that incident, who had reportedly been denied a transfer to his home town, shot himself but survived his injuries, according to the ISNA news agency.
Military service of two years is mandatory for Iranian men when they turn 19.
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