The Revolutionary Guards said they had brought down a ScanEagle – one of the smaller, less sophisticated drones employed by the Americans.
Rear Admiral Ali Fadavi told the Fars news agency that the drone had conducted several reconnaissance flights over the Gulf in recent days.
But the US Navy said none of its drones was missing in the Middle East.
The ScanEagle drone, which has a has a 10ft (3m) wingspan, is a low-cost, long-endurance aircraft built by Insitu, a subsidiary of Boeing.
Rear Adm Fadavi said that “such drones are usually launched from large warships”.
Fars said the drone was captured “in the last few days” without giving further details.
A spokesman for US Naval Forces Central Command in Bahrain said: “The US Navy has fully accounted for all unmanned air vehicles operating in the Middle East region.
A year ago, Iranian TV broadcast pictures of an American RQ-170 Sentinel drone
“Our operations in the Gulf are confined to internationally recognised water and air space.
“We have no record that we have lost any ScanEagles recently.”
Last month, the US said Iranian warplanes had shot at a US surveillance drone flying in international airspace. Iran said the aircraft had entered its airspace.