The report Saturday described the assailants as "Takifiri gunmen", a term previously used to describe ISIS.
"Several gunmen began shooting from behind the stand during the parade".
State media say Islamist militants are thought to be behind the attack.
There has been no claim of responsibility for the attack in the city of Ahvaz.
IRGC spokesman Ramezan Sharif said the attackers were affiliated with a terrorist group supported by Saudi Arabia, Press TV said.
The state-run IRNA news agency reported that the wounded included a woman and a child but did not elaborate.
In footage shown on Iranian television, paramedics could be seen helping a person in military uniform lying on the ground at Ahvaz's Quds, or Jerusalem, Boulevard.
Bloodied troops could be seen in combat fatigues, helping each other walk away in images from Iranian news service ISNA.
At least 18 people were killed and more than 50 wounded in the 2017 attack that saw gunmen carrying Kalashnikov assault rifles and explosives storm the parliament complex where a legislative session had been in progress, starting an hours-long siege.
Iran's Armed Forces staged the countrywide military parades to mark the Sacred Defense Week on the 38th anniversary of the onset of the Iraqi imposed war on the Islamic Republic back in 1980.