The liquefied petroleum gas tanker NV Sunshine came under fire in the strategic waterway, the IRGC said in a statement carried by Iran's Tasnim news agency.
"Any ship using an unauthorised transit route will be pursued throughout the region, and its punishment will be inevitable," Tasnim quoted the IRGC as saying.
The vessel was travelling along a southern shipping route near the coast of Oman, according to the report.
The IRGC has previously laid blame for incidents in the strait on the US military, accusing Washington of interfering in the decisions of shipping and insurance companies and paying "large bribes" to induce compliance.
In recent months, the US Navy has been escorting civilian merchant vessels with their transponders switched off along the route in an effort to restore oil and gas shipments.
Iran, which has sought to tighten control over the strait, considers the route "illegal" and demands that ships instead pass along the Iranian coast.
Separately, the British maritime security agency UKMTO reported an incident near the coast of the United Arab Emirates on Friday.
It was not immediately clear whether the two reports referred to the same incident.
The Strait of Hormuz, a vital waterway for global energy trade, has been the scene of repeated attacks on shipping during the war between Iran and the United States.
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