Nobody was injured and both ships appeared to suffer only superficial damage from the early Monday morning accident, according to a spokesman for the US Navy 5th Fleet, Commander Jeffrey Breslau.
It was the US Navy's second collision with a civilian vessel in the Gulf in 14 months.
The USS Philadelphia hit the Turkish-flagged M/V Yaso Aysen at around 2200 GMT on Sunday, said a statement from the 5th Fleet Headquarters in Bahrain.
The collision happened about 50km northeast of Bahrain, said Breslau.
The Philadelphia was conducting surface operations on its way to Bahrain for a scheduled port visit, the navy said.
Afterwards, the submarine continued to Bahrain where inspectors will check it for damage.
The submarine's nuclear-powered propulsion plant was not damaged in the crash, according to the navy.
Breslau said the Turkish ship, a bulk carrier, suffered minor damage to its hull just above the water line.
The ship weighed anchor at the site of the crash, and a US Coast Guard vessel was sent to offer help, Breslau said.
An initial inspection found the cargo vessel to be seaworthy.
The cause of the collision was under investigation, he added.
The submarine is part of a fleet of US and allied navy vessels conducting what are called "maritime security operations" in the Gulf against the smuggling of weapons and drugs and movement of "terrorists".