The collision involving the USS Porter and the Panamanian-flagged bulk oil tanker M/V Otowasan occurred at approximately 1 am local time, the US Navy said in a statement.
The damage to the Porter is being evaluated and the incident is under investigation, the Navy added.
The USS Porter is on a scheduled deployment to the US 5th Fleet, which is based in Bahrain.
The Strait of Hormuz, located at the mouth of the Persian Gulf, is where one-fifth of the world's oil is routed. Tensions have risen there over Iran's threats to block tanker traffic in retaliation for tighter sanctions by the West.