The US Geological Survey said the tremor - which measured 6.1 on the Richter scale - hit 33 miles southwest of Bandar Abbas, where the country's main naval base is located, along with an oil refinery.
State television reported at least 10 aftershocks, but it is not yet clear if any oil facilities have been damaged.
The deaths happened on Qeshm island, just off the country's coast in the Strait of Hormuz.
Some 100,000 are said to live on the island, which is situation near the United Arab Emirates.
"So far we have been conducting rescue operations in about seven villages and we have no estimate of the damage," Ahmad Esfandiari, from Iran's Red Crescent, told state television.
The head of the local branch of the national disasters office said there was some damage and there had been power cuts to some parts of the island.
The powerful tremor was also felt in Dubai.
Ex-pat Briton Angharad Irving-Jones, 35, was on the 13th floor of a building in the city's financial sector when the quake struck.
She told Sky News Online: "The whole building shook. Then tables started to sway and I grabbed a corner of a table. The blinds started to bang against the window glass.
"The table was sliding from wall to wall.
"It was so intense that we were feeling dizzy and very nauseous.
"It was like we were out at sea. The building was swaying and it did not seem to stop for ages."
Iran sits over several major faults and is prone to frequent earthquakes, some of which have had devastating effects.
In 2003, a quake hit the country's southeast killing 31,000 people and destroying the city's ancient mud-built citadel.
Earthquake hits iran
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Draw from your past....... but don't let your past draw from you
Yama, The world is changed. I feel it in the water. I feel it in the earth. I smell it in the air. Much that once was..... is lost. For none now live who remember it.
For all your Computer needs www.btlogic.co.uk