Lt Ian McConnaughey of the Bahrain-based 5th Fleet says the incident happened on Monday.
He says the Iranian boat came within 1,000 meters (yards) of the USS Mahan.
The lieutenant says the Mahan "made several attempts to contact the Iranian vessel by bridge-to-bridge radio, issuing warning messages and twice sounding the internationally recognised danger signal of five short blasts with the ship's whistle, as well as deploying a flare to determine the Iranian vessel's intentions."
The Iranian vessel later sailed away.
The US Navy and Iran routinely have tense encounters in the waters of the Persian Gulf.