Iran is marking the anniversary of the beginning of the 1980-88 war with Iraq with several parades across the nation.
This is a developing story and will be updated accordingly.
Fars news agency said the attack started at 09:00 local time (06:30 BST) and appeared to involve at least two gunmen.
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. There has been no claim of responsibility for the attack in the city of Ahvaz.
ISNA published photographs of the attack's aftermath, with bloodied troops in dress uniforms helping each other walk away.
Ahvaz is the capital of Iran's oil-rich Khuzestan province.
The state-run IRNA news agency put the number of wounded at 20, including a woman and a child. The province has a large ethnic Arab community, many of them Sunni, the Muslim denomination to which IS adheres and which is a minority in Shiite Iran. The semi-official Tasnim news agency said at least eight member of the Guard had been killed.
Early reports Saturday described the assailants as "Takifiri gunmen", a term previously used to describe the Islamic State group.
On Friday, the IRGC and the Iranian army also held a joint aerial military drill in the Gulf, where the USA keeps maintains a fleet to protect oil shipping routes, as reported by Reuters. The assault shocked Tehran, which largely has avoided militant attacks in the decades after the tumult surrounding the Islamic Revolution.
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