But the manager of the restaurant, called Halal KFC, said it had nothing to do with the US company.
Police justified the decision saying it was operating under a false licence.
The closure comes amid concerns amongst hardliners about growing Western influence in Iran as relations with a number of countries improve.
"The shutting down of Halal KFC was due to a misunderstanding," Abbas Pazuki, the manager of Halal KFC, told the Tasnim News Agency.
He said police had thought the restaurant was a branch of the American KFC.
"We are part of a brand known as Halal KFC, which comes from Turkey. It belongs to Muslims and its target market is Muslim nations," said Pazuki.
He said the Turkish brand was a "rival of the American KFC".
Earlier reports suggested the authorities closed down the first branch in Tehran of the better known KFC.
Ali Fazeli, head of the Iranian chamber of commerce, confirmed that the Iranian KFC has no connection with KFC in the US, according to ILNA press agency.
"In accordance with orders from the Supreme Leader, we do not give any authorisation to Western brands" in the fast food sector, Fazeli said.
The state media reported the opening of the restaurant as a first sign of creeping US influence, the BBC's Kasra Naji says.
Hardliners believe the recent agreement on curbing Iran's nuclear programme, reached between Iran and Western powers, may become a vehicle for softening Iran's anti-Americanism, opening the floodgates of foreign influences, our correspondent adds.
Several Western countries are seeking closer business ties with Tehran following the agreement.
Only a day after it opened, Iran has shut down what officials reportedly thought was a branch of the US fast food giant Kentucky Fried Chicken.