"So far no casualties have been reported," said local governor Alireza Khorani, quoted by Fars news agency.
"There were some houses and electricity poles damaged. Rescue teams have been dispatched to the area," he said.
There were reports on social media in Saudi Arabia that the quake, at a depth of 10.2 miles, was felt in the kingdom's eastern province, across the Gulf from Iran.
Iran's Arab neighbours across the Gulf have often raised concern over the reliability of the Bushehr plant and the risks of radioactive pollution in case of a major earthquake.
But Iran and Russia, which built the Bushehr plant, insist it respects international standards under the supervision of the IAEA, the UN nuclear watchdog.
Iran stands on several seismic fault lines. A massive quake in December 2003 struck the southern city of Bam, killing 26,000 people and destroying its ancient mud-built citadel.