The US Geological Survey registered the quake at 0738 IST, measured at 85 kilometres (52 miles) southeast of the town of Minab, located in the southern Hormuzgan province and off the Strait of Hormuz.
The quake was registered at a depth of 36.44 kilometres (22.64 miles), the USGS said.
A local emergency official said a two-year-old died of serious injuries. "The child passed away on route to hospital," Mohammad Shekari was quoted by the ISNA news agency.
Iran sits astride several major fault lines and is prone to frequent earthquakes, some of which have been devastating.
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Head of Iran's National Institute for Oceanography Vahid Chegini said today's quake was unlikely to spark a tsunami in the Gulf or the Sea of Oman.
"The chances of a tsunami because of today's quake are remote as the quake was inland," Chegini told the Mehr news agency.
Mozafar, who heads Iran's Red Crescent rescue corps, said rescue teams were dispatched to Hormuzgan's remote area hit by the quake.
Media reports said electricity and telephone connection had been cut, while rescue teams were attempting to open blocked roads to the quake-hit areas.
Last month, the biggest earthquake to hit the country in 50 years, measuring 7.8 killed a woman and injured more than a dozen other people in the southeast.
At least 40 people were killed across the border in Pakistan where hundreds of mud homes were levelled.
Also in April, another quake struck near Iran's Gulf port city of Bushehr, killing at least 30 people.
The UN's atomic agency said there was no damage to Iran's only and Russian-built nuclear power plant at Bushehr. Iran said the plant continued its operations as normal.