Mohamed Hasan al-Bahrani, Al Jazeera's Tehran bureau chief, said that available information pointed to a bomb going off in the mosque after Maghreb and Isha prayers.
The explosion took place in the section where males were praying, according to reports.
Fars said the force of the blast shook houses more than one kilometre away.
It quoted a police official as saying that the bomb was a "hand-made" device that had been planted in the mosque.
"There was a huge blast and the whole place lit up. Everyone started shouting and screaming and tried to help each other," Marzian Mohammadnejad, a witness, told Iran's English language Press-TV.
No group or individual has claimed responsibility for the explosion.
Fars reported that the mosque hosted weekly speeches denouncing Wahaabism – a version of Sunni Islam - and the outlawed Bahai faith. Iran is a predominantly Shia country.
Iran had been the cradle of the Bahai faith in the middle of the 19th century. After the Islamic revolution in 1979, the faith was banned and the country's constitution does not recognise it as a religious minority.
Last year, Bahai communities abroad said some of followers of the faith were detained in Shiraz while working with poor communities there.
Shiraz is close to a number of ancient sites popular with tourists.
The last major bombing in Iran occurred in the south-eastern city of Zahedan in February 2007.
Thirteen members of Iran's elite Revolutionary Guard died in that blast, and a Sunni group called Jundallah, or God's Brigade, claimed responsibility for the attack.