The indefinite ban, announced Monday on state-run television, highlighted the continuing tension between Iran and the West over Tehran's nuclear program.
In remarks Saturday, Ahmadinejad had defended Iran's right to continue nuclear research. State media have complained since the news conference that CNN translated his words as "nuclear weapons" instead of "nuclear technology" or "nuclear energy."
"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 Culture and Islamic Guidance Ministry statement read on state-run television.
CNN acknowledged the mistake in its U.S. broadcast.
"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."
The network added that it had apologized.
CNN told viewers it had not been officially notified about the ban.
Mohammad Hossein Khoshvaght, director-general of foreign press and media at the 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.
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.
A CNN spokesperson did not immediately return a call Monday to the network's Atlanta headquarters seeking comment.
The ban comes amid meetings by international diplomats over how to react to Iran's removal last week of U.N. seals from its main uranium enrichment facility and resumption of research on nuclear fuel. Western nations suspect Tehran is trying to develop nuclear weapons; Iran insists its program is for peaceful energy purposes.
The CNN 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 has not yet been allowed to return to Iran.