File Photo: The earthquake struck close to the port city of Bandar Abbas at about 12 pm GMT. AP
The 6.4 and 6.3 magnitude earthquakes hit at 15 kilometres (9.3 miles)in Hormozgan province, the Iranian seismological centre said.
A 22-year-old man was killed by a falling electricity pole, Iranian Red Crescent chief Mehdi Valipour told state television.
He said several teams have been deployed to assess the damage.
The public broadcaster aired live footage from the area showing trucks stopped on the road, having been shaken by the tremor.
Walls of buildings cracked in the southern port city Bandar Abbas, the capital of Hormozgan province, local governor Azizollah Konari told journalists.
"The earthquakes lasted a long time and frightened people," state television said.
The United States Geological Survey (USGS) measured the tremors at magnitudes of 6 and 6.3.
Situated on the edge of several tectonic plates and crossing various fault lines, Iran is an area of strong seismic activity.
Iran's deadliest quake was a 7.4-magnitude tremor that struck in 1990 killing 40,000 people in the north of the country.