Annan had planned to visit the Islamic Republic in mid-November during a swing through the Middle East beginning next week, presumably to talk about Iran's nuclear policy.
But remarks by Iranian President Mahmoud Ahmadinejad in late October calling for the destruction of Israel prompted the Secretary-General to cancel his trip.
"The secretary-general and the Iranian government have mutually agreed that this is not an appropriate time for him to travel to Iran," UN spokesman Stephane Dujarric said on Friday.
"In light of the ongoing controversy, it would have been difficult to advance the agenda that he had wanted to discuss with the Iranian leadership," Dujarric said.
Ahmadinejad was condemned by world leaders when he said "the establishment of the Zionist regime was a move by the world oppressor against the Islamic world", in a speech at the World without Zionism conference in Tehran on 26 October.
Ahmadinejad said "Israel must
be wiped off the map"
"As the Imam said, Israel must be wiped off the map," Ahmadinejad added, referring to Iran's revolutionary leader Ayat Allah Khomeini who died in 1989.
Annan, who had previously rebuked the Iranian president, told reporters on Thursday that "no one in the international community defended what the Iranian president said and the Security Council itself issued a statement".
But in Tehran, a Foreign Ministry source contended it was Iran, not Annan, who wanted the trip rescheduled "to a more appropriate time in the future".
According to the country's official news agency Irna, Iran said recent comments made by Annan were "under the influence of American officials and were not interpreted well in Tehran".