The hull of the Sabiti was hit by two separate explosions about 100 kilometers off the Saudi port city of Jeddah, the state-owned company said on October 11.
The state-run IRNA news agency and others relied on an online news report for their stories, while the semi-official ISNA news agency quoted an anonymous source with direct knowledge of the incident.
It said the blasts were "probably caused by missile strikes".
The Nour news agency, believed to be close to the Revolutionary Guard Corps, said the crew of the oil tanker was safe.
The United States had alleged that Iran attacked oil tankers near the Strait of Hormuz, at the mouth of the Persian Gulf, something denied by Tehran.More news: Trump Says U.S. Holds ‘Most Dangerous’ Islamic State Terrorists in Syria
More news: Women in attendance in Iran’s World Cup qualifier, first time since 1981
More news: Kim Kardashian says Prince Harry and Duchess Meghan are 'changing the world'
The U.S. Navy's 5th Fleet, which oversees the region, did not immediately respond to a request for comment.
There was no immediate word from Saudi Arabia on the reported attack.
Iranian media earlier reported that an explosion had set the oil tanker on fire.
Tensions have been high between regional foes Iran and Saudi Arabia since an attack on the kingdom's two oil facilities on 14 September that caused fires and damage, shutting down 5.7 million barrels per day of production - more than five percent of global oil supply.
The incident comes amid growing tensions between Iran and the USA and its allies in the Persian Gulf following a series of suspected sabotage attacks off the coast of the United Arab Emirates in mid-May. Riyadh blamed Tehran. Iran, which supports the Houthis in Yemens war, has denied any involvement.