There was no report of the execution on Iran's media and judiciary officials could not be reached for comment on Thursday, the start of the weekend in the country.
"This is the fourth confirmed execution of a child offender in Iran in 2020. The execution of child offenders is categorically prohibited under international law and Iran is under the obligation to abide by this prohibition," the UN human rights office said in a statement.
"UN High Commissioner for Human Rights Michelle Bachelet strongly condemns the killing of Mohammad Hassan Rezaiee. We are also dismayed that this execution took place despite interventions ...with the Government of Iran on this issue," the statement said.
Amnesty International said on Twitter that Rezaiee had been convicted based allegedly on forced confessions and had spent 12 years on death row.
Persons convicted of crimes as juveniles have been executed regularly since the establishment of the Islamic Republic in 1979.
Under Iran's laws, the age for adulthood is determined by puberty, 15 for boys and nine for girls, but a judge is expected to determine the maturity of the defendant in capital punishment cases.
When there is a discrepancy between domestic law and international legal obligations, Iranian authorities have turned to domestic law.