There were no immediate reports of damage or injuries.
Iran's official IRNA news agency says the epicentre of the quake was the town of Emam Hassan and that it struck around 4:30 am today.
The Bushehr nuclear power plant, which went online in 2011 with Russian help, is built to withstand earthquakes of magnitude 8.
In 2013, a magnitude-6.1 temblor killed at least 37 people in an area of the same province where today's quake struck.