A sentence - for blinding an Iranian man - was scheduled to be carried out at noon (0730 GMT) on Saturday at the judiciary hospital in Tehran in the presence of a physician and representatives of the coroners' office and the prosecution.
"The execution of qesas (retribution in kind) of Majid (Movahedi)... has been postponed to an unknown date," ISNA news agency reported on Saturday on its website just hours before the appointed time.
Movahedi was sentenced to be blinded in both eyes in February 2009 for having hurled acid in the face of Ameneh after she repeatedly spurned his offer of marriage.
His victim, who has been the driving force behind the sentence, had travelled to the Iranian capital from Spain in the expectation of it being carried out and had even suggested she was ready to do the blinding herself.
"I still strongly stand with the carrying out of the qesas. I want qesas, I will become more serene," she told ISNA on May 11.
"This serenity will not stem from the culprit suffering hardship and pain but that (with the carrying out of the sentence) there is the probability of more deterrence regarding those who want to commit this crime," she said.
The Islamic sharia code in force in Iran provides for eye-for-an-eye-style retributive justice, most commonly for murder.
Bahrami, who was 24 when she met Movahedi in 2002, now lives in Spain where she has been undergoing medical treatment for her disfigurement for years. She is blind in both eyes and still has serious injuries to her face and body.