Residents across the Gulf in the United Arab Emirates reported feeling the tremor.
Oil facilities 'unscathed'
The US Geological Survey said the earthquake was 53km west-southwest of Bandar Abbas and at a depth of 55km.
At least ten aftershocks followed the earthquake, the largest of which measured 4.8 on the Richter scale.
A state news report said that the earthquake caused power cuts and damage on Qeshm, which is home to about 100,000 people.
"More than 100 houses in villages of Qeshm have been damaged between 30 per cent and 50 per cent," Gholam Ali Daneshvar, an official on Qeshm, was quoted as saying by the official IRNA news agency.
But a senior Iranian oil official said that oil facilities in Bandar Abbas had not been damaged by the earthquake.
"Fortunately, there was no damage to the oil industry's facilities at Bandar Abbas," Hojjatollah Ghanimifard, vice president for investment affairs at the National Iranian Oil Company, said.
Iran is particularly prone to earthquakes as it sits over several earth fault lines. At least 31,000 were killed in an earthquake at the southeastern city of Bam in 2003.