According to reports, the invading vessel changed course and returned to the coast after the Alborz destroyer warned it would target the vessel in seconds.
"If the terrorists ignored our warning, they would be killed with the first bullets of Alborz," the ship’s commanding officer, Commodore Hassan Maqsoudlou, was quoted as saying by Iran’s Fars news agency.
The incident took place as Iran's 34th fleet of warships is in the Gulf of Aden on an anti-piracy mission, and as Iranian cargo ships carrying humanitarian aid head to Yemen.
US and other western naval ships have on several occasions approached the Iranian flotilla in violation of international rules.
In the latest such case, US and French warships and military aircraft changed course in the Gulf of Aden on Saturday night after being warned by an Iranian flotilla to stay away.