The bombings came days before the presidential vote and were the deadliest in Iran in more than a decade.
At least four women were among those killed in the explosions in Ahvaz, capital of the south-western Khuzestan province. At least two of the explosions were caused by car bombs, witnesses said.
Gholamreza Shariati, deputy provincial governor for security affairs, said the bombers were seeking to undermine public participation in Friday’s presidential elections.
Television pictures showed the blast sites with heavily damaged buildings and blood on the ground. The force of the explosions also damaged cars in the streets. Mr Shariati said 36 people, including eight police officers, were injured.
After the first three blasts, disposal experts tried to defuse a fourth bomb but failed, and it exploded, injuring one officer.
Amir Hossein Motahar, director of security at the Interior Ministry, said one bomb went off in front of the Ahvaz governor’s office and another next to the city’s housing department.
The third bomb blew up in front of the residence of the head of the provincial radio and television station, he said. The fourth bomb was placed nearby.
Mr Shariati said intelligence and security officials were investigating the bombings, which targeted “Iran’s territorial integrity as it was on the verge of presidential elections.”
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.
Officials confirmed one death but opposition groups said more than 20 demonstrators had been killed. Some 250 were arrested.
The protests were sparked after copies of a letter allegedly signed by Vice President Mohammad Ali Abtahi circulated. The letter ordered the relocation of non-Arabs to the Ahvaz to make them the majority population. Mr Abtahi denied writing the letter.
Arabs make up about 3% of Iran’s population of 69 million. Persians account for 51% and other minorities comprise the remainder.