Iranian President Mahmoud Ahmadinejad, a regular at the assembly since he took office in 2005, will give his final speech there on Wednesday and will address a meeting on the "rule of law" on Monday.
But of the 160-or-so visas requested by the Iranian delegation two months ago, about 20 were turned down, Fars said.
It gave no reason, but many Iranian officials are subject to travel bans under sanctions related to Iran's nuclear program.
In Washington, the US State Department had no immediate comment on the matter.
Fars did not name the two ministers who were denied visas and said Ahmadinejad would be accompanied by his chief of staff Esfandiar Rahim Mashaie and Foreign Minister Ali Akbar Salehi.
Fars named two of those banned from going to New York as members of Ahmadinejad's staff: Mohammad Shaikhan, in charge of communications and information, and Mohammad Jafar Behdad, in charge of political affairs.
Ahmadinejad, whose second and final term in office ends next year, has used previous UN speeches to defend a nuclear program he insists is peaceful and to make verbal attacks on Israel, the United States and Europe.
He has questioned the historical truth of the Holocaust and cast doubt on whether Islamist hijackers were really responsible for the attacks of September 11, 2001.
Most Western envoys walk out of the UN chamber during his speeches, in protest.
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Good on you USA.