CNN's simultaneous translation of Ahmadinejad's lengthy news conference on Saturday included the phrase "the use of nuclear weapons is Iran's right".
In fact, what the Iranian president said was that "Iran has the right to nuclear energy", the official IRNA news agency reported.
CNN later apologised for its mistake.
Iran denies any intention of seeking nuclear weapons, saying it wants atomic technology merely for the generation of electricity.
CNN acknowledged the mistranslation in a statement released from its headquarters in Atlanta on Monday and said it had apologised for the error on CNN International, CNNUSA and all other CNN outlets that had used the mistranslation.
In addition, the US news group said it had expressed its regrets to the Iranian government and Iran's ambassador to the United Nations.
"Despite this there are reports today, Monday, that Iran has banned us from the country. CNN is very disappointed that this action has been taken," CNN group said.
"So far it's not clear whether it was something pre-planned or a mistake. Therefore, we will ban its activities [in Iran] for the time being."
Mohammad Hossein Khoshvaght, Iran's Culture and Islamic Guidance Ministry
Mohammad Hossein Khoshvaght, director of foreign media at Iran's Culture and Islamic Guidance Ministry, welcomed CNN's apology.
"But so far it's not clear whether it was something pre-planned or a mistake," he told state television. "Therefore, we will ban its activities [in Iran] for the time being."
He said a restoration of CNN's right to work in Iran would depend on an assessment of the broadcaster's future coverage of the Islamic state.
ISNA said Iran's Culture and Islamic Guidance Ministry deemed the error a "violation of professional ethics".
CNN does not have a permanent bureau in Iran but a local journalist is a contributor to the network and visiting correspondents are occasionally given permission to enter the country on short assignments.
The ban came as Christiane Amanpour, CNN's Iranian-born chief international correspondent, was in Iran to report on the nuclear issue.