The Thailand-flagged bulk carrier Mayuree Naree was targeted on Wednesday and damaged about 20km north of Oman, two maritime security sources said.
The United Kingdom Maritime Trade Operations said later, referring to the incident, that the fire had been extinguished and there was no environmental impact.
Necessary crew remained on the vessel.
Earlier, the Japan-flagged container ship One Majesty had sustained minor damage from an unknown projectile 46km northwest of Ras Al Khaimah in the United Arab Emirates, two maritime security sources said.
Its crew members were safe and the vessel was sailing towards a safe anchorage, the sources said.
A third vessel, a bulk carrier, was also hit by an unknown projectile about 80km northwest of Dubai, maritime security firms said.
The projectile had damaged the hull of the Marshall Islands-flagged Star Gwyneth, maritime risk management company Vanguard said, adding that the vessel's crew were safe.
Traffic through the Strait of Hormuz, a key artery accounting for about 20 per cent of global oil and gas supply, has dropped rapidly since the Iran conflict began on February 28.
The latest incidents increase the number of ships that have been attacked since the conflict began to at least 14.
