Experts on board to investigate suspected it was a "terrorist attack", the agency said, citing unidentified sources.
The explosion has caused heavy damages and oil is spilling in the Red Sea, unnamed sources told ISNA.
Iran's national tanker company (NITC) says the fire has been put out and the oil spillage reduced to a minimum, Iranian news site Iran Front Page reports. "The situation is under control", Nour reported.
"We believe that considering the current conditions in the region, the Saudis have come to the conclusion that the war can not decide the fate".
Several attacks on oil infrastructure in the Gulf have occurred in recent months amid heightened tensions across the Middle East.
The reported explosion comes after the USA has alleged that Iran attacked oil tankers near the Strait of Hormuz, something denied by Tehran.
The tanker Sinopa was built in 1999 and is Iranian flagged vessel.
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.
Tehran and Washington have been at loggerheads since the United States previous year withdrew from a 2015 nuclear deal between Iran and world powers.
Iran, which supports the Houthis in Yemen's war, has denied any involvement.
Oil attacks: What's next for Saudi Aramco and world oil markets?