Reports say Ali Naderi, 21, was executed earlier this month after being found guilty of a murder he committed when he was 17.
An OHCHR statement said the death penalty cannot be legally imposed for crimes committed by people under 18.
It cited the Convention on the Rights of the Child and the International Covenant on Civil and Political Rights, saying Iran is a party to both agreements.
Naderi's was the first reported juvenile execution since September 2011.
The OHCHR called on Iran to restrict the use of the death penalty and reduce the number of offenses for which it may be imposed.