Five villages were damaged when the quake hit Qeshm Island at 1:53 pm local time and was felt for more than 10 seconds.
"The toll stands at nine dead and we are not expecting it to increase.
Between 70 and 80 people were injured," said Qeshm island governor Heydar Alishbandi after touring the affected area.
The Gulf island, home to about 100,000 people, is situated off the coast from the large port city of Bandar Abbas.
"Three helicopters are taking the injured to hospitals in Bandar Abbas and ferries are available if needed. Tents and other relief supplies have been sent to the area," he said.
Another tremor, measuring 5.5 on the Richter scale, hit the same area hours later at 8:41 pm, the official Irna agency said, although there were no immediate reports of damage or casualties from the second quake.
Iranian state television put the intensity of the first quake at 5.9 on the
Richter scale, the US Geological Survey put the magnitude slightly higher at 6.1 while a seismic observatory in the French city of Strasbourg put it at 5.6.
Mr Alishbandi said five villages suffered damage of between 40 and 70 percent, adding that most of the homes "are made of mud bricks so are now unsafe."
Bam quake
The rocky and barren island was hit almost two years after the southeastern city of Bam, situated 300 kilometres (190 miles) to the north, razed in December 2003 by a 6.7 degree quake that left more than 31,000 people dead.
Qeshm, located 1,150 kilometres southeast of Tehran, has a busy commercial and fishing port and is also a popular weekend sunshine getaway for Iranian tourists.
However the governor said the island's main town, also called Qeshm, was undamaged.
The affected villages were identified as Gabardin, Tonban, Karvan,
Tourian and Khaldin, which are all situated in the less densely populated west of the island.
Iran sits astride several major faults in the earth's crust, and is prone to frequent earthquakes.
In February, a quake measuring 6.4 on the Richter scale hit the southern town of Zarand, killing 612 people and wounding around 1,400.
Mehdi Zareh, the head of Iran's Seismic Research Centre, said there was no tsunami risk from the latest quake.
"Because the Persian Gulf is not very deep, a tsunami is not expected," he told the student news agency ISNA.
Contacted by telephone, a hotel worker in Qeshm described the quake as "very strong".
"We were panicked. I saw an injured person with blood on their clothes being taken to a local hospital," said the hotel worker, who asked for her name not to be used.
The quake was also felt across the Gulf in the United Arab Emirates where residents fled high-rise office and apartment buildings.