The agency did not say whom Iranian officials suspect Online Cigarettes Store USA of launching the missiles.
Lt. Pete Pagano, a spokesman for the U.S. Navy's 5th Fleet overseeing the Mideast, said authorities there were "aware of reports of this incident," but declined to comment further.
Benchmark Brent crude oil rose over 2% in trading Friday to reach some $60.40 a barrel.
The reported attack comes after the U.S. has alleged that in past months Iran attacked oil tankers Newport Pleasure near the Strait of Hormuz, at the mouth of the Persian Gulf, something denied by Tehran.
Friday's incident could push tensions between Iran and the U.S. even higher, more than a year after President Donald Trump unilaterally withdrew America from the nuclear deal and imposed sanctions now crushing Iran's economy.
The mysterious attacks on oil tankers near the Strait of Hormuz, Iran shooting down a U.S. military surveillance drone and other incidents across the wider Middle East followed Trump's decision.
The latest assault saw Saudi Arabia's vital oil industry come under a drone-and-cruise-missile attack, halving the kingdom's output. The U.S. has blamed Iran for the attack, something denied by Tehran. Yemen's Houthi rebels, whom the kingdom is fighting in a yearslong war, claimed Newport 100s Box that assault, though analysts say the missiles used in the attack wouldn't have the range to reach the sites from Yemen.