The agency named the alleged ringleader as Mahmud Makharmeh, 29, a computer engineering student and said his accomplices were Nur Makharmeh, 22, and Diaa Sarakhneh, 22.
It did not say if the Makharmehs were related.
The statement said the group "was run by Iranian intelligence and was recruited and financed by an Iranian intelligence operative living in South Africa."
"It has been learned that Iranian intelligence has been using South Africa as a significant centre for locating, recruiting and operating agents against Israel," the English- language statement added.
He was ordered to recruit suicide attackers and gunmen and to collect and pass on intelligence to his Iranian contacts, who paid him $8,000 dollars, the Shin Bet said.
It said that all three were "recently" charged in an Israeli military court.
Mahmud Makharmeh was charged with contact with a hostile foreign organisation, receiving enemy funds and attempting to join an illegal organisation.
The other two were charged with attempting to join an illegal organisation.
Prime Minister Benjamin Netanyahu said the Hebron group's alleged plot was just the latest attempt by Iran to attack Israel.
"This is not the first time. They are trying various methods, and in various fields, to attack the State of Israel," the office of the Israeli leader quoted him as saying in an English-language statement.
In 2015 an Israeli court sentenced an Iranian-born Belgian citizen to seven years in prison after convicting him of spying for Tehran posing as a businessman.
He was sentenced for "aiding an enemy during war" and "espionage" on behalf of Iran's elite Republican Guard.
Iranian academic Ahmadreza Djalali is currently facing execution in Tehran after his October conviction on a charge of spying for Israel.
Djalali has said he is being punished for refusing to spy for Iran while he was working in Europe.
(This story has not been edited by Business Standard staff and is auto-generated from a syndicated feed.)