On Saturday, President Mahmoud Ahmadinejad defended Iran's right to continue nuclear research. State media have complained since the speech that CNN used the translation "nuclear weapons" instead of "nuclear technology."
The ban by the Culture and Islamic Guidance Ministry was read in a statement on state-run television.
"Due to mistranslation of the words of President Mahmoud Ahmadinejad during his press conference, activities of the American CNN in Tehran are banned until further notice," said a statement by the Culture and Islamic Guidance Ministry read on state-run television.
CNN acknowledged the mistake.
"CNN quoted Mahmoud Ahmadinejad as saying that Iran has the right to build nuclear weapons," the network said in its report of the ban. "In fact he said that Iran has the right to nuclear energy. He added that, quote, a nation that has civilization does not need nuclear weapons and our nation does not need them. CNN has clarified what the Iranian president said and apologized here on the air to the Iranians directly, as well as on the air."
CNN told viewers it had not been officially notified about the ban.
Mohammad Hossein Khoshvaght, director-general of foreign press and media at the culture ministry, told The Associated Press that the ban followed a review of "past activities of CNN," not limited to Saturday's speech. He would not elaborate.
"We have decided to wait for their future coverage on Iran to make any further judgment" on whether to lift the ban, he said.
CNN correspondent Christiane Amanpour has been reporting from Iran for the last week. Khoshvaght said she was scheduled to leave on Tuesday even before the ban was announced.
He said the ban extended to CNN's stringers in Iran.
The ban marks the second time in a year that Iran has acted against an international broadcaster because of its coverage. Last April, Iran suspended the nationwide operations of Arab TV network Al-Jazeera, accusing it of inflaming violent protests by the Arab minority in its southwest.
Al-Jazeera was believed to have been the first news outlet to broadcast news of the violence unrest in Khuzistan province, which erupted after rumors spread of an alleged government plan to move non-Arabs into the oil-rich city of Ahvaz.
Al-Jazeera has not yet been allowed to return to Iran.
By Nasser Karimi