State television said the explosion damaged two storerooms aboard the unnamed oil tanker and caused an oil leak into the Red Sea. It did not elaborate.
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.
All reports said the reported explosion happened off the coast of Jiddah on the Red Sea.
The U.S. Navy's 5th Fleet, which oversees the region, did not immediately respond to a request for comment.
The reported explosion comes after the U.S. has alleged that in past months Iran attacked oil tankers near the Strait of Hormuz, at the mouth of the Persian Gulf, something denied by Tehran.
The explosion could push tensions between Iran and the U.S. even higher, more than a year after President Donald Trump unilaterally withdrew America from the nuclear deal and imposed sanctions now crushing Iran's economy.
The mysterious attacks on oil tankers near the Strait of Hormuz, Iran shooting down a U.S. military surveillance drone and other incidents across the wider Middle East followed Trump's decision.
The latest assault saw Saudi Arabia's vital oil industry come under a drone-and-cruise-missile attack, halving the kingdom's output. The U.S. has blamed Iran for the attack, something denied by Tehran. Yemen's Houthi rebels, whom the kingdom is fighting in a yearslong war, claimed that assault, though analysts say the missiles used in the attack wouldn't have the range to reach the sites from Yemen.