The incident raises fresh concerns within the Obama administration about Iranian military aggression in crucial Gulf oil shipping lanes.
The drone was in international airspace east of Kuwait, U.S. officials said, adding it was engaged in routine maritime surveillance.
Although the drone was not hit, the Pentagon is concerned.
Two U.S. officials explained the jets were part of Iran’s Revolutionary Guard Corps force, which has been more confrontational than regular Iranian military forces.
The Obama administration did not disclose the incident, which occurred just days before the presidential election on November 1, but three senior officials confirmed the details to CNN.
The officials declined to be identified because of sensitive intelligence matters surrounding the matter.
The drone’s still and video cameras captured the incident showing two SU-25s approaching the Predator and firing its onboard guns.
The Iranian pilots continued to fire shots that went beneath the Predator but were never successful in hitting it, according to the officials.