Iran's state broadcaster cited the Islamic Revolutionary Guard Corps as saying the Togo-flagged oil tanker Trend was struck due to what it described as an "illegal attempt" to pass through the strait.
The Guard's navy warned that vessels attempting to pass through the strait without authorisation would face "destruction," the broadcaster said.
Iran has asserted control over the waterway since the US and Israel launched the war on February 28.
The United Kingdom Maritime Trade Operations (UKMTO) reported a "security incident" overnight involving a vessel 16 nautical miles northeast of Khasab, Oman, which lies on the other side of the strait.
The crew was safe and no environmental impact was reported, the monitor said.
It was not clear whether the UKMTO report referred to the attack claimed by Iran.
The US military has been escorting some commercial ships through the strait off Oman as the threat of Iranian attacks continues.
Separately, the UKMTO said a tanker in the strait was hit by an "unknown projectile," causing a fire that was later extinguished.
The crew was reported safe, with no immediate indication of environmental damage, it said.
Hundreds of thousands of Iranians filled the streets of Tehran in the biggest rally since the war began in February, pledging to take up arms as "Janfaday-e Iran," or those "who sacrifice their lives for Iran".
Iran's government has sought to rally the people and stress unity even as the economy worsens under a US naval blockade of Iranian ports and new US sanctions.
Some participants trampled flags of the US and Israel.
Others chanted "Death to America" and "Death to Israel".
