The aircraft, which belonged to Strike Fighter Squadron 147, was in a holding pattern while preparing to land aboard the carrier Nimitz, officials with U.S. Navy Central Command said.
The unarmed Iranian QOM-1 drone approached, coming within 100 feet vertically and 200 feet laterally of the aircraft, ignoring radio calls to stay clear of aircraft operations.
"The F/A-18E maneuvered to avoid collision with the QOM-1, resulting in a lateral separation of approximately 200 feet and a vertical separation of approximately 100 feet," said Lt. Chloe Morgan, a NAVCENT spokeswoman, in a statement.
"The dangerous maneuver by the QOM-1 in the known vicinity of fixed-wing flight operations and at coincident altitude with operating aircraft created a collision hazard and is not in keeping with international maritime customs and laws," she said.
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Morgan said Tuesday's incident was the 13th unsafe or unprofessional maritime interaction with Iranian forces to date this year.
It comes just weeks after a Navy patrol craft, the USS Thunderbolt, was forced to fire warning shots from its .50-caliber machine guns in July to stop the dangerous approach of vessels belonging to the Iranian Revolutionary Guard Corps Navy.
"That is a capability that the entire world is getting, and Iran is no different," he told Military.com in an interview aboard the Bush. "These aren't small, radio-controlled drones. They're reconnaissance."
The Nimitz recently arrived in the region to replace the Bush, which is expected to return shortly to its homeport in Norfolk.