The official in the Iranian interior ministry’s Natural Disasters Unit said the quakes struck the district of Zahrindasht, near Jahrom in the southern province of Fars. The area is situated approximately 800 km south of the capital Tehran and near the city of Shiraz.
"Some villages were hit. There are some dead, but we don’t have any precise figure at this stage," the official said, adding that the area was sparsely populated.
The first quake struck at 9:36 pm (1706 GMT), and the second at 10:12 pm (1742 GMT). State media said the first quake lasted 12 seconds and cut off electricity supplies to the area.
State radio said rescue teams had reached the area but quoted a provincial official as saying the "number of dead is not very high".
In France, the Strasbourg earthquake observatory said it detected a single quake measuring 5.5 on the open-ended Richter scale. The epicentre was in the region of Hajjiabad.
Earthquakes are frequent in Iran, and about 950 have hit the country since 1991, killing a total of 17,600 people and injuring another 53,500.