"The judiciary decided not to carry out the sentence in public because of some security issues," Ebrahim Hamidi, a judiciary official in Sistan-Baluchestan, said.
Families of Jundollah victims were, however, present at the execution to help alleviate "their pain," Hamidi said.
Iranian state Press TV also accused Rigi of drug dealing, murder and armed robbery. He was captured in Pakistan in 2008 and extradited to Iran.
Iran also alleges the Jundollah has ties with al-Qaeda.
Iranian officials accuse the United States, Britain and Pakistan of supporting Jundollah in order to destabilise Iran, a charge these countries vehemently deny.
Jundollah says it is fighting for the rights of Sunni Muslims in Iran's impoverished Balcuhestan province which borders on Pakistan and Afghanistan.
Rigi was the brother of Abdolmalek Rigi, the alleged leader of Jundollah who is awaiting trial in an Iranian prison.
Abdolmalek was arrested by Iranian security forces February 23 2010.
"He is only 30 years old," our Tehran correspondent said. "And he faces execution like his brother."