Rear Admiral Ali Fadavi told the Fars news agency that the drone had conducted several reconnaissance flights over the Gulf in recent days.
The US said it was looking into the reports. The ScanEagle drone 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".
The Revolutionary Guards are an elite unit of the Iranian military which operate their own naval forces.