"The execution has apparently gone ahead despite Iran's moratorium on execution by stoning, a moratorium that had been in effect since 2002," said Jose Diaz of the Office of the High Commissioner for Human Rights.
He said Arbour's office had received numerous reports that Jafar Kiani was executed near Tehran on July 5, and was waiting for official confirmation.
The reported execution comes two weeks after international pressure caused Iranian officials to delay carrying out the sentence against the man and his female companion, Mokarrameh Ebrahimi, who was still scheduled to be executed according to Diaz.
He said the couple had reportedly been imprisoned for 11 years.
"Stoning is in clear violation of international law," Diaz said, adding that the high commissioner considered this form of execution to be a form of cruel, inhuman or degrading treatment or punishment that is prohibited under an international treaty which Iran has signed.
"International law also limits the death penalty to only the most serious, violent crimes," he said.