The UK Maritime Trade Enforcement Agency (UKMTO) reported that the fire started from the engine room of a tanker 37km northeast of Sohar, Oman.
UKMTO reported 1 death but did not specify the cause of the fire.
Both US and Iranian forces have attacked commercial ships in the Strait of Hormuz since the ceasefire agreement took effect in April.
Thousands of ships are still trapped on this important waterway when both sides implement a double blockade.
Also according to UKMTO, on June 10, an incident occurred off the coast of Yemen, in which an armed high-speed train shot at a cargo ship.

The UK Maritime Trade Organization, which monitors waterways in and around the Gulf Arab countries, said that just hours earlier a gunfight occurred between the attacking group and the security team on the cargo ship. The incident is being investigated and is causing much concern.
On June 9, the Secretary-General of the International Maritime Organization (IMO) warned ships not to try to pass through the Strait of Hormuz when there is no reliable security guarantee.
I am increasingly concerned about reports that ships continue to try to pass through the Strait of Hormuz without any credible security guarantees," IMO Secretary-General Arsenio Dominguez said.
Mr. Dominguez informed that sailors have been killed, injured and arrested in recent incidents in the context that the regional security situation is still very unstable and lacks reliable assurance for safe movement.
My top concern is the safety and lives of the sailors in the current situation," he said, noting sailors should not take risks.
The head of the IMO emphasized that captains and shipping companies must be responsible for planning their journeys and assessing risks within the framework of international safety and security management.
There is no commercial or operational consideration that can justify letting sailors face such a level of danger. Protecting their lives must always be a top priority," he said.
He also called on all parties involved to act responsibly and urged all parties to restrain actions that could endanger civil sailors.
According to IMO data, as of June 9, there have been 42 confirmed maritime incidents since the Iranian conflict broke out at the end of February, leading to 11 confirmed deaths related to sailors.