The statement added that the Los Angeles-class submarine's nuclear reactor "remains in a safe condition" along with the propulsion plant.
US military officials said that a naval P-3 aircraft carried out a search operation in the area but spotted no debris in the water or vessels in distress.
The incident follows an August collision between a US guided missile destroyer and an oil tanker.
An American nuclear-powered attack submarine has collided with an "unidentified" fishing ship in the Persian Gulf shortly after passing through the Strait of Hormuz, says a statement by US Navy's Fifth Fleet.
The USS Jacksonville "struck a vessel while operating in the Persian Gulf" at about 5:00 a.m. local time (0200 GMT) on Thursday, the statement added.
One of the submarine's periscopes has been damaged in the collision, a Navy official said on condition of anonymity.
"Jacksonville then surfaced from periscope depth to ascertain if there was any damage to the unidentified vessel," the Bahrain-based Fifth Fleet said.
"The vessel continued on a consistent course and speed offering no indication of distress or acknowledgement of a collision."