"Police closed the 'KFC' restaurant as it didn't have authorisation and had been operating under a false license," reported the news site of Iran's Young Journalist Club, which is affiliated with state television.
The fast food joint, KFC Halal, had only been open for three days, the site said.
A nuclear deal signed between Iran and world powers in July has seen several Western countries seek closer business ties with Tehran, where years of punishing economic sanctions could be lifted if the Islamic republic keeps its side of the bargain.
The rapprochement has seen US fast food chains such as McDonald's and KFC reportedly explore the possibility of opening branches in Iran, something that has stirred debate among conservative Iranians.
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"No American fast food chain has a restaurant in Iran," Ali Fazeli, head of the Iranian chamber of commerce, was quoted as saying by the ILNA press agency.
"Food products from Iranian KFC have nothing to do with KFC" in the United States, he said.
"In accordance with orders from the supreme leader (Ayatollah Ali Khamenei), we do not give any authorisation to Western brands" in the fast food sector, Fazeli added.
Khamenei on Tuesday called on Iranians to remain "vigilant" against the United States, which he said had not changed despite striking a deal with Tehran.
Most of Iran's lawmakers voted Monday to keep the slogan "Death to America" despite the nuclear accord.
Although Khamenei has since endorsed the deal, known officially as the Joint Comprehensive Plan of Action, he accused Washington in September of using nuclear talks as a means of imposing its own agenda on Tehran.