The claim was made on Iranian state TV Monday and included an image of a purportedly downed aircraft.
According to the report, the country's Revolutionary Guard captured the Boeing-designed ScanEagle after it entered Iranian airspace over the Persian Gulf. But the report doesn't say exactly when they got it.
A Navy spokesman said no U.S. drones have gone missing recently in the Middle East. Analysts said it's possible it was pulled from the sea in the past and the nation chose to show it off now.
Last month, Iran claimed that a U.S. drone had violated its airspace. Pentagon said the unmanned aircraft came under fire - at least twice but was not hit - and that the Predator was over international waters.
Last year, Iran claimed it brought down a CIA spy drone and studied its technology. The RQ-170 Sentinel drone was captured almost intact. The U.S. asked for it back, but Iran refused.
The Associated Press contributed to this report.