The decision in effect bars Hamid Aboutalebi from taking up the role at the UN, which is based in New York.
Hamid Aboutalebi was linked to the student group that took dozens of people hostage at the embassy in Tehran.
President Barack Obama has come under intense pressure from the US Congress not to allow him to enter the country.
Earlier this week, the White House told the Iranian government its selection of a one-time student revolutionary to be UN ambassador was “not viable”.
A spokesman for Iran’s mission to the UN, Hamid Babaei, described the decision as “regrettable” and said it contravened international law.The US House of Representatives and the Senate have both voted in favor of a bill barring Hamid Aboutalebi from the US. It still requires the signature of the president before it can become law.
Iran says Hamid Aboutalebi is one of its most experienced diplomats and stands by his nomination.
White House spokesman Jay Carney said on Friday the UN and Iran had been told “that we will not issue a visa to Mr. Aboutalebi”.
He did not say whether President Barack Obama would sign the bill but said the president shared the sentiments of Congress.
In an interview with an Iranian news site last month, Hamid Aboutalebi said he was not part of the group that took over the US embassy and was only later asked to translate for the students.
The 52 Americans were held for 444 days during the crisis.
It is believed the US has never before denied a visa for a UN ambassador and correspondents say there is concern among diplomats about the precedent that could be set.
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