State television said the assault, which also wounded 20 people, targeted a stand where Iranian officials were gathered to watch an annual event marking the start of the country's 1980-88 war with Iraq.
Four militants carried out the attack and two of them were killed, according to ISNA.
Foreign Minister Mohammed Javad Zarif blamed the bloodshed on "regional terror sponsors", language that usually refers to Iran's enemies Saudi Arabia and Israel, and "their United States masters", and vowed that Tehran would respond decisively.
"Security forces have restored security in the area but the parade has totally been disrupted", a reporter on the scene for Iranian state television said by phone in a live broadcast.
Iran's Tasnim news agency, citing a local official, reported that at least 10 people had been killed, including a journalist.
State television immediately described the assailants as "takfiri gunmen", a term previously used to describe the Islamic State group.
Ahvaz, in southwestern Khuzestan province, is home to the small Arab minority in Iran, which is mainly ethnic Persian.
Bloodied troops could be seen in combat fatigues, helping each other walk away in images from Iranian news service ISNA.
At that point it marked the only attack by the Sunni extremists inside of Shia Iran, which has been deeply involved in the wars in Iraq and Syria, where the militants once held vast territory.
Saturday's attack comes after a coordinated June 7, 2017 Islamic State group assault on parliament and the shrine of Ayatollah Ruhollah Khomeini in Tehran. At least 18 people were killed and more than 50 wounded in the attacks. The province in the past has seen Arab separatists attack oil pipelines.