The attack was the latest targeting a vessel moving through the narrow mouth of the Persian Gulf, through which a fifth of all traded oil and natural gas once passed in peacetime.
Iranian state television said the liquefied natural gas tanker came under attack after ignoring warnings but did not directly claim the assault.
Tehran has repeatedly declared that only its approved route through the strait is safe and is suspected of attacking other ships that have used another route close to the Omani shore.
The United Kingdom Maritime Trade Operations centre said the tanker had been hit near Limah, Oman, in the strait early on Tuesday.
The centre said the projectile hit the port side of the vessel while travelling south out of the strait toward the Gulf of Oman.
A report from US outlet Axios, citing two American officials, said Iran's Revolutionary Guards fired at least two missiles at commercial ships transiting through the Strait of Hormuz on Monday night.
Two commercial ships suffered significant damage but had no casualties, the report said.
Iran's Revolutionary Guards warned ships via maritime radio over the weekend that "our missiles and drones are ready to fire at you", the Wall Street Journal reported on Monday, quoting from a recording it obtained.
One of the vessels under attack appeared to be Al Rekayyat, a liquefied natural gas tanker owned and managed by Nakilat, also known as Qatar Gas Transport Company Ltd, which operates one of the world's largest LNG shipping fleets, the WSJ said.
The ship had been hit on the port side at the top of the engine room and was at the mouth of the strait, in the Gulf of Oman, when it was attacked, the WSJ reported.
"Engine room fire and full of smoke. Unable to assess further damage. All crew are safe and mustered on the starboard side," the WSJ quoted from a recording.
The US is eager to press ahead with negotiations with Iran aimed at fully reopening the strait, rolling back Tehran's disputed nuclear program and reaching a permanent end to the war launched in February.
Iran and the United States agreed as part of an interim deal to allow ships to pass in the strait without paying charges for 60 days.
But Tehran insisted it must control the routes of the vessels and later charge fees for passage, upending decades of practice in the waterway.
The data firm Kpler reported that over the last weekend at least 108 ships crossed through the strait using various routes.
Talks between Iran and the US appear to be on hold until after the burial of Iran's late supreme leader Ayatollah Ali Khamenei, who was killed at the beginning of the war.
Mourners have held signs calling for the death of US President Donald Trump.
Authorities flew Khamenei's body to the Shi'ite seminary city of Qom overnight, where mourners honoured him on Tuesday.
Iranian state television aired live images from a helicopter of hundreds of thousands of people walking toward Jamkaran Mosque, just south of Qom, for a funeral service for Khamenei.
Images of Khamenei and his son, Iran's new Supreme Leader Ayatollah Mojtaba Khamenei, were displayed on banners and posters held by mourners.
Mojtaba Khamenei has yet to make an appearance in the funeral ceremonies, which are unfolding over several days. He is believed to be in hiding after reportedly being wounded in the airstrike that killed his father.
Authorities have shut down streets, airspace and daily life for the mourning, which began on Saturday and will end on Thursday as Khamenei is buried at the Imam Reza shrine in Mashhad, his birthplace. Khamenei was 86.
With Reuters
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