The monkey returned alive after travelling in a capsule to an altitude of 120 kilometers (75 miles) for a sub-orbital flight.
"This success is the first step towards man conquering the space and it paves the way for other moves," General Vahidi said, but added that the process of putting a human into space would be a lengthy one.
"Today's successful launch follows previous successes we had in launching (space) probes with other living creatures (on board)," he added.
"The monkey which was sent in this launch landed safely and alive and this is a big step for our experts and scientists."
Iranian state television showed still pictures of the capsule and of a monkey being fitted with a vest and then placed in a device similar to a child's car-seat.
Iran announced in mid-January its intention to launch a monkey into orbit as part of "preparations for sending a man into space," which is scheduled for 2020.