The quake, whose epicentre was in the Masjed Soleiman area of Khuzestan province, hit at 11:30 am (0700 GMT) at a depth of 17 kilometres, the national seismological centre reported.
The region was rattled by seven aftershocks, the strongest of which measured 4.7 magnitude, it said.
At least 45 people were injured, the head of Iran's relief and rescue organisation, Morteza Salimi, told state TV.
"One citizen at Masjed Soleiman also passed away due to a heart-attack after the earthquake," Salimi said.
In nearby cities and villages affected by the quake, there were "only minor cracks in buildings" and roads to some villages were cut off.
Iran sits on top of major tectonic plates and sees frequent seismic activity.
In November 2017 a 7.3-magnitude tremor in the western province of Kermanshah killed 620 people.
In 2003, a 6.6-magnitude quake in southeast Iran decimated the ancient mud-brick city of Bam and killed at least 31,000 people.
Iran's deadliest quake was a 7.4-magnitude tremor in 1990 that killed 40,000 people in northern Iran, injured 300,000 and left half a million homeless.
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