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.
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.
Military service of two years is mandatory for Iranian men when they turn 19.