In an article published in the newspaper Business Day on Wednesday, the chief rabbi said that Goldstone's report had "unfairly done enormous damage to the reputation and safety of the state of Israel and her citizens".
He said that while he understood Goldstone's "anguish", the right to protest was a tenant of "free democracy".
Goldstone hit back with a letter to the newspaper on Thursday, in which he said that the rabbi had "brazenly" politicised his grandson's bar mitzvah and criticised him for having not "reached out" to his family.
It was, he said, a "questionable and unfortunate approach" that was inconsistant with the chief rabbi's rhetoric on open synagogues.
Goldstone's report, commissioned by the UN Human Rights council, found both Israel and Hamas had committed war-crimes during last year's war on Gaza and called on both sides to investigate the allegations.
But his findings caused fury amongst pro-Israeli groups, who said they were biased against Israel.
Goldstone, a South African Jew, was personally targeted in a smear campaign following the report's publication.
South African Jewish leaders said that the report had caused "a lot of anger" in the Jewish community.
But others said threats to picket the bar mitzvah were "disgraceful".
Doron Isaacs, a South African NGO leader who has campaigned for a just solution to the Israeli-Palestinain conflict, last week told Al Jazeera that the picket plan was a deliberate intimidation attempt.
"There is a belief amongst right-wing Zionist organisations that defaming and humiliating Jewish critics of Israeli policy will set an example that would intimidate others into silence," he said.