The report said the epicentre of the quake, which occurred at 1:52 pm, was near the Gulf island of Qeshm.
There were no immediate reports of damage or casualties.
The quake was also felt across the Gulf in the United Arab Emirates where residents fled high-rise office and apartment blocs.
"I took my baby and ran down the 10 flights to the street," one alarmed resident of Dubai told AFP.
The temblor was also felt in the neighbouring UAE emirates of Ras al-Khaima and Sharjah, residents said.