The boats are said to have ignored flares and a smoke float dropped by helicopter, so the destroyer fired off a trio of shots.
The US Navy fired three warning shots at four Iranian boats after they closed in at speed on Sunday, say defence officials.
It happened in the Strait of Hormuz after the Iranians did not respond to requests by the USS Mahan to slow down, and instead continued asking the ship questions.
A helicopter dropped a smoke float and the destroyer launched flares but the boats continued at speed, according to the officials speaking anonymously to Reuters.
The Islamic Revolutionary Guard vessels are said to have come to within 800m of the Mahan, which was escorting two other US ships.
The Strait of Hormuz is a narrow passage that leads from the Persian Gulf to the Arabian Sea.
A large portion of the world's oil passes through the strait on tankers, making it a strategically important route.
There have been similar incidents between the US Navy and Iranian boats in the area, with Iran threatening to close off the route in 2011.
President-elect Donald Trump said in September that any Iranian vessels that harass American ships in the Gulf would be "shot out of the water".