ABC News said no one was injured in Thursday's incident and the nuclear reactor was not damaged.
A Navy official told ABC News the periscope was likely sheared off by a fishing trawler.
He said the crew was conducting normal operations "when they felt a shudder." The crew then pulled up the periscope and discovered the damage.
ABC News said the submarine then traveled by surface to the U.S. naval base in Bahrain where officials are conducting a damage assessment.
ABC News said the accident is under investigation.