There has been no independent confirmation that the video broadcast late on February 6 is genuine.
It shows what Iranian officials said is a U.S. base inside Afghanistan and other aerial shots.
In comments accompanying the video, the chief of the aerospace division of the Islamic Revolutionary Guards Corps, Amir Ali Hajizadeh, said Iran has been able to "definitively access the data of the drone."
He also said Iranian forces had been put on alert after the drone's capture in case the United States launched air strikes to destroy it.
U.S. officials have previously confirmed that a Sentinel drone had been monitoring Iranian nuclear and military activities.