Images purporting to show an unnamed US warship were shown on television.
Iran's navy commander praised the operation for getting so close to a warship "to get such accurate footage of the combat units of foreign forces".
The US said an Iranian drone had flown over one of its carriers recently, but did not say if it was this incident.
It had not posed a risk to the USS Harry S Truman, but the move was "abnormal and unprofessional", Reuters news agency quoted a US navy spokeswoman as saying.
Nicole Schwegman said that incident had occurred on 12 January, which is the same day Iran briefly detained 10 US sailors who had entered Iranian territorial waters by mistake.
The report by Iran's state Irinn news channel did not say when the surveillance drone had made its flight except to say it was on the third day of a naval exercise.
The Associated Press news agency said this suggested it had happened on Friday, as Iran's naval drill began earlier this week.
An Iranian light submarine also closely participated in the surveillance operation, Iran's state-run Irna news agency reported.
Adm Habibollah Sayyari, Iran's navy chief, told state TV it was a sign of the "bravery, experience and the scientific capabilities of our drone operators".
International sanctions against Iran over its nuclear programme were lifted this month, somewhat easing its relations with the West.
But within a few days, the US had imposed new sanctions related to Iran's ballistic missile programme.
Iran said the sanctions, which prevent 11 entities and individuals linked to the programme from using the US banking system, had "no legal or moral legitimacy".
Iran flew an unarmed drone over a US aircraft carrier and took "precise" photographs during a naval drill in the Gulf, its state broadcaster said.