The blasts took place during a ceremony to commemorate top commander Qassem Soleimani who was killed by a U.S. drone in 2020.
Officials blamed terrorists, adding that dozens more were wounded in the attack.
Iranian state television reported a first and then a second blast during an anniversary event at the cemetery where Soleimani is buried.
An unnamed official told state news agency IRNA that: "Two explosive devices planted along the road leading to Kerman's Martyrs' Cemetery were detonated remotely by terrorists."
No group immediately claimed responsibility for the attacks.
Videos aired by Iranian media showed dozens of bodies strewn around with some bystanders trying to attend to survivors and others hurrying to leave the blast area.
Head of the Kerman Red Crescent Society Reza Fallah told state television that his organization was investigating.
"We are now evacuating the wounded and injured in the area. The crowd is huge and the job is quite hard all the paths to there are blocked."
The assassination of Soleimani and Tehran's retaliation by attacjubg two Iraq military bases that house U.S. troops, brought the United States and Iran close to a full-blown conflict in 2020.
Soleimani had been chief commander of the overseas arm of Iran's Revolutionary Guard Corps.
He ran clandestine operations in foreign countries and was a key figure in Iran's long-standing campaign to drive U.S. forces out of the Middle East.
