An unidentified military official quoted in the report warned of a strong and crushing response to any violations of the country's airspace by American drone aircraft.
"An advanced RQ-170 unmanned American spy plane was shot down by Iran's armed forces. It suffered minor damage and is now in possession of Iran's armed forces," IRNA quoted the official as saying.
No further details were published.
The U.S.-led coalition in Afghanistan said in a statement the aircraft may be an American drone that its operators lost contact with last week while it was flying a mission over neighboring western Afghanistan.
Iran is locked in a dispute with the U.S. and its allies over Tehran's disputed nuclear program, which the West believes is aimed at developing nuclear weapons. Iran denies the accusations, saying its nuclear program is entirely peaceful and that it seeks to generate electricity and produce isotopes to treat medical patients.
The type of aircraft Iran says it downed, an RQ-170 Sentinel, is made by Lockheed Martin and was reportedly used to keep watch on Osama bin Laden's compound in Pakistan as the raid that killed him was taking place earlier this year.
The surveillance aircraft is equipped with stealth technology, but the U.S. Air Force has not made public any specifics about the drone.
Iran said in January that two pilotless spy planes it had shot down over its airspace were operated by the United States and offered to put them on public display. In July, Iranian military officials showed Russian experts several U.S. drones they said were shot down in recent years.
Also in July, Iranian lawmaker Ali Aghazadeh Dafsari said Iran's Revolutionary Guard shot down an unmanned U.S. spy plane that was trying to gather information on an underground uranium enrichment site.
Dafsari said the pilotless plane was flying over the Fordo facility near the holy city of Qom in central Iran but the Guard denied the report, saying its air defenses had only hit a test target.
Iran publicly confirmed for the first time in Feb. 2005 that the United States has been flying surveillance drones over its airspace to spy on its nuclear and military facilities.
The Islamic Republic holds frequent military drills, primarily to assert an ability to defend against a potential U.S. or Israeli attack on its nuclear facilities.
Tehran has focused part of its military strategy on producing drones for reconnaissance and attacking purposes.
Iran announced three years ago it had built an unmanned aircraft with a range of more than 600 miles (1,000 kilometers), far enough to reach Israel.
Ahmadinejad unveiled Iran's first domestically built unmanned bomber aircraft in August 2010, calling it an "ambassador of death" to Iran's enemies.