Last year, a quake that struck near the Iran-Iraq border in November killed at least 361 people.
In many areas people had returned to their homes by daybreak after the initial panic subsided and the aftershocks petered out.
Pirhossein Koulivand told state TV about the deaths and injuries early Friday morning.
Rescuers have been dispatched to the region, officials said.
Up to 30 homes were destroyed near the epicentre, it added. Shallow earthquakes tend to cause more damage.
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A United States Geological Survey photo showing the location of a magnitude 5.9 natural disaster which struck at a depth of 10km, almost 60m from Hastrud, Iran, today.
The USGS issued an alert warning that "significant casualties are likely and the disaster is potentially widespread".
Iran sits where two major tectonic plates meet and experiences frequent seismic activity.
A 6.6-magnitude quake in the south-eastern Iranian city of Bam in 2003 killed around 26,000 people.
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