The British navy-affiliated agency UKMTO said on Sunday it had a report of a projectile hitting a vessel as it moved through the strait.
Local authorities evacuated the crew after a fire broke out following the attack, the agency said on Sunday.
UKMTO's report came the day after Saudi Arabia said it had temporarily closed its east-west pipeline as a precaution after a drone attack Baghdad and Riyadh said had originated in Iraq, where Iranian-backed militias operate.
Ongoing attacks in the widening Middle East war could send energy prices even higher after a week in which Brent crude surged back above $US100 ($A139) a barrel.
The 1200km east-west pipeline across the Arabian Peninsula has served as the main route for global supplies of Middle East oil for the past six months while the Strait of Hormuz has been largely shut by war.
It has been moving four to five million barrels per day - four to five per cent of global supply - sparing Saudi Arabia the brunt of the disruption that has crippled other Gulf oil and gas exporters.
No one has claimed responsibility for the pipeline strikes.
Satellite images showed black smoke rising from an area of the pipeline south of Medina.
The attack resulted in some injuries and damage that was being assessed, the Saudi Foreign Ministry said without detailing the impact on exports.
US President Donald Trump, visiting Ireland to attend a golf tournament at one of his resorts, said Iran was probably to blame.
On Saturday, the Saudi Civil Defence said in a statement a projectile fired by the Houthis had injured two people in Jazan region and damaged several buildings, including a mosque.
Iranian state media reported an Iranian commercial vessel was struck off its southern coast early on Sunday, killing one person and wounding three others, without giving further details.
Houthi-run Al Masirah TV said on Sunday Saudi Arabia carried out three air strikes on the al-Rubaie area in Taiz province in southwest Yemen.
There was no official confirmation from Saudi Arabia.
On Saturday, the Houthis said there had been 129 Saudi air strikes in the previous 48 hours.
Oil prices shot up in the past week and the retail price of diesel in the US surged as the US and Iran fired on tankers and the Houthis in Yemen rapidly advanced along the Red Sea, potentially giving Tehran leverage over both of the region's main oil-shipping corridors.
Washington now faces a dilemma over whether to help the Saudis fight the Houthis, risking expansion of the war.
Saudi Arabia's de facto ruler, Crown Prince Mohammed bin Salman, phoned Trump on Thursday and asked for US military help fighting the Houthis, three sources told Reuters.
They said the prince was told Washington would not intervene directly for now but would help with intelligence.
Trump confirmed on Saturday he had spoken to the crown prince, and said the Houthis had also phoned his administration and asked Washington not to become directly involved in the conflict.
Four Yemeni government sources told Reuters the Houthis had seized the strategic island of Perim on Friday in the middle of the Bab el-Mandeb strait - the "Gate of Tears" at the southern entrance to the Red Sea.
The Houthis have been attacking Saudi ships in the area since declaring a blockade in July and targeting its other oil facilities.
There have been no talks between the US and Iran to end the conflict since a June agreement that collapsed within weeks.
