The Sabiti was hit in the morning about 60 miles (96 km) from the Saudi port of Jeddah, Iran’s state agency IRNA reported. The National Iranian Tanker Company (NITC) said the ship was damaged but now heading to the Persian Gulf, denying reports it was set ablaze.
The incident is the latest involving oil tankers in the Red Sea and Persian Gulf area.
Iran’s national television, citing the national oil company, said the tanker was hit by missiles while denying a report they came from Saudi Arabia.
NITC said in statement on its website that “the blasts were probably caused by missile strikes” and it was investigating the source.
"All the ship's crew are safe and the ship is stable too," NITC said, adding those on board were trying to repair the damage.
National television broadcast images from the Sabiti’s deck saying they were taken after the blasts, but there was no visible damage.
Iran’s Foreign Ministry said the tanker was attacked "from a location close to the corridor it was passing, east of the Red Sea".
Ministry spokesman Seyyed Abbas Mousavi described the attack as “a dangerous adventure”, warning that all the responsibilities fall on those behind it.
Mousavi expressed concern about the maritime pollution caused by the massive oil spill in the region after damage inflicted on the vessel’s tanks.
“All the responsibilities for the act, including the extensive environmental pollution in the region, fall on those behind the dangerous adventure.”
He also noted that a probe is being conducted on the details of the attack and those behind it, and the results will be announced once it is done.
According to Iranian national television, the blasts could have been the result of a "terrorist attack."
The Red Sea is a major global shipping route for oil and other trade, linking the Indian Ocean with the Mediterranean via the Suez Canal.
There was no claim of responsibility for Friday’s incident, which follows attacks on tankers in the Persian Gulf in May and June, as well as strikes on Saudi oil sites in September.
The United States, embroiled in a row with Tehran over its nuclear plans, has blamed Iran for those incidents. Tehran has denied having a role in any of the attacks.
Saudi Arabia had no immediate comment on Friday’s reports. The US Navy’s Fifth Fleet, which operates in the region, said it was aware of the reports but had no further information.
The International Energy Agency warned against market complacency after the attack, as it noted that a quick recovery of output and fears of a global economic slowdown had already seen prices recover from the September attacks on Saudi oil infrastructure.
Refinitiv ship tracking information indicated the Sabiti, a Suezmax class tanker, was in the Red Sea and heading south under its own power, bound for Larak, off Iran’s southern Persian Gulf coast.
Russia said it was too early to assign blame for the tanker explosion. China, the top buyer of Iranian oil, said it hoped all parties would work to uphold peace and stability in the region.
China called on all parties to "exercise restraint" in the "highly complex and sensitive" situation.
Oil prices climbed 2% after reports of the tanker incident, with benchmark Brent and US West Texas Intermediate crude futures both rising more than $1 a barrel. Brent was trading around $60 a barrel on Friday.
Crude prices had eased after spiking above $70 in response to the Sept. 14 attacks on Saudi oil sites, which shut down 5.7 million barrels per day (bpd) of production, about half of Saudi output and roughly 5% of global supply. Output has since been restored. Yemen’s Houthi group claimed responsibility for the Saudi attacks.
Industry sources said Friday’s incident off the Saudi coast could drive up shipping costs, which have already surged.
Disruption to shipping through Red Sea would affect oil passing through the Suez Canal or SUMED crude pipeline, which has capacity for 2.34 million bpd and which runs parallel to the canal. It is used by tankers that cannot navigate the waterway.
Reuters, AFP and Press TV contributed to this story.