The center's website says the temblor hit at 1:36 p.M. local time today and its epicenter was the town of Jam, some 880 kilometers south of the capital, Tehran.
In 2013, a magnitude-6.1 quake killed at least 37 people and injured hundreds more in the same region.
Bushehr, which went online with Russian help in 2011, is built to resist earthquakes up to magnitude 8.0.
Iran experiences frequent earthquakes. In 2003, some 26,000 people were killed by a magnitude-6.6 quake that flattened the historic southeastern city of Bam.