The explosions rocked Ahvaz, capital of Khuzestan province bordering Iraq, and damaged several buildings.
Interior Ministry spokesman Jahanbaksh Khanjani told journalists there were up to four attacks and "several dead".
The Fars news agency said five people had been killed and 25 wounded in the blasts at about 9am. State television put the number of wounded at 30 but did not say how many had been killed.
The attack comes ahead of presidential elections set for Friday.
Ahvaz was the site of two days of violent demonstrations in April after reports circulated of an alleged plan to decrease the proportion of Arabs in the area.
More than 250 people were arrested in the protests. Officials at the time confirmed one death, but opposition groups said more than 20 demonstrators had been killed.
The protests were sparked after circulation of copies of a letter allegedly signed by Vice President Mohammad Ali Abtahi that ordered the relocation of non-Arabs to the city to make them the majority population.
Abtahi denied writing the letter.
Arabs make up about 3% of Iran's population while Persians account for nearly 51% of the population of 69 million.
Bomb explosions have been a rare occurrence in Iran since the end of the 1980-88 Iran-Iraq war.