The tremors, measuring 5.6 and 5.8 degrees on the Richter scale, also shook several other cities, including Jahrom, and the neighboring villages but there was no immediate report on probable casualties and property damage.
Two of the injured were taken to neighboring cities for hospitalization and the rest received treatment for minor injuries, the official said.
"A number of villages were damaged in the tremors, the worst hit being Shahr-e Pir, Deberan, Deh-No, Darreh Shur and Darva," Mousavi said.
The quakes severely damaged power and telephone lines, disrupted water supply and destroyed a police outpost in the village of Deberan, he added.
Seismological bases of Tehran University's Geophysics Institute registered the first quake of 5.6 intensity at 21:36 (1706 GMT) Thursday. The second temblor, measuring 5.8 degrees, struck at 22:12 (1742 GMT), they said, adding the tremors were succeeded by 15 after-shocks.
"An earthquake of this intensity has been unprecedented in the city (of Zarrin-Dasht) and fortunately villagers were not inside their homes because of the hot weather.
"This helped the earthquakes not leave significant death doll," the governor said.
Relief workers were dispatched to the cities of Darab, Fasa, Jahrom, Estahban and Shiraz and a task force office was set up to coordinate relief and rescue operations in the affected regions, he said.
He said there was urgent need for food, blankets and tents.
"At present operations to rush relief and remove debris are under way and experts are estimating the exact extent of damage incurred," Mousavi said.
Zarrin-Dasht, 300 km to the southeast of Shiraz, has a population of 70,000 people.
Iran sits on some of the world's active seismic faultlines and tremors of mild magnitude are almost a daily occurrence.
Since 1991, at least 17,000 Iranians have been killed and more than 53,000 others injured in earthquakes.
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