"The army's air defence shot down two... RQ-11 drones," Rear Admiral Amir Rastegari told state television and Fars news agency, adding that the army was carrying out "research" on the downed unmanned aircraft.
He said the first had been brought down in Shahrivar 1390 (August-September 2011) and the second in Aban 1391 (October-November 2012), but gave no details of their location.
He did not offer proof for the claim.
Iran has in the past claimed to have hunted down a number of US drones, showing detailed images of the alleged spoils.
In December it said it had captured a small US ScanEagle drone in its airspace above the Gulf, which the US navy denied.
A year before that, it claimed to have captured a much bigger and more sophisticated CIA stealth drone, an RQ-170 Sentinel.
The AeroVironment RQ-11 type aircraft that Rastegari said had been shot down is a small, hand-launched and remote-controlled drone used by US military intelligence, and has also been adopted by some US allies.
It has a range of over six miles (10 kilometres) and can fly at up to 60 miles (95 kilometres) per hour for 80 minutes.
Rastegari made the announcement after a six-day Iranian naval exercise in the Gulf of Oman and the Strait of Hormuz, through which a third of the world's marketed oil passes.
Several surface-to-air missiles were fired as part of the manoeuvres, according to Iranian media.