An oil tanker belonging to the National Iranian Oil Company (NIOC) was hit and damaged by two missiles on Friday, Iranian state news IRNA reported.
The missiles were "possibly" fired from Saudi soil, Saheb Sadeghi, head of the public relations of the National Iranian Tanker Company, told state-run Press TV.
Reports that the missiles were fired from Saudi territory were later dismissed by NIOC, as reported by IRNA.
Iran has not offered any publicly available evidence for the incident. The ship is still moving and travelling south, according to the tracking service Marine Traffic.
No Iranian government officials have blamed the attack on any side at this stage.
Commenting on the incident, Iranian Foreign Ministry spokesman Abbas Mousavi said according to the semi-official Fars News Agency: "Those behind this dangerous adventurism are responsible for the consequences of such act."
The tanker was 60 miles (96 kilometres) from the Saudi port of Jeddah on the Red Sea when the incident occurred, damaging its body, IRNA reported.
According to the news service, the resulting explosions caused oil to leak into the Red Sea.
Iran's Press TV also tweeted Friday: "Report: Explosion in #Iranian tanker has set vessel on fire near #Saudi port city of #Jeddah."
All the tanker's crew members are safe, IRNA reported. Investigators are looking into the sources of the missiles.
News of the incident caused oil prices to rise on Friday. Prices for Brent Crude jumped 2% to just over $60, while WTI Crude climbed nearly 2% to $54.
A series of attacks on oil tankers and production facilities in the region has increased tensions in recent months.
In September, Saudi Arabia's Abqaiq oil processing facility -- the largest of its kind in the world -- was attacked in a series of drone strikes which halved the country's production.
Houthi rebels claimed responsibility for the attack, but both Saudi and US investigators claimed "with very high probability" that it was launched from an Iranian base.
Shortly after that attack, President Donald Trump said the US was "locked and loaded." He added that the US was waiting on Saudi Arabia to find out "under what terms we would proceed."
Speaking to CNN, Iranian Foreign Minister Javad Zarif denied responsibility for the September attack and warned of "all-out war" if the US or Saudi Arabia conducted military strikes against his country.
The drone strikes followed attacks on tankers in the Strait of Hormuz in July, including the capture of the UK-flagged oil tanker Stena Impero by Iran. The vessel was eventually released from the Iranian port of Bandar Abbas in late September.