According to the Iranian naval force, one tanker was near the Strait of Hormuz. The second was reportedly sailing east of the strategic waterway.
Both vessels allegedly caught fire after hitting sea mines. The IRGC Navy said both oil tankers had switched off their navigation and positioning systems.
It claimed the vessels were attempting to pass through maritime routes that Iran considers unauthorized.
The Iranian force warned that ships entering restricted waters in violation of its maritime regulations could face the risk of striking sea mines.
The Iranian statement came after local media reported explosion-like sounds in several areas of Hormozgan province.
According to the British Broadcasting Corporation (BBC), the IRGC Navy issued its statement following these reports.
However, the claims about the tankers and the cause of the fires have not been independently verified.
The IRGC Navy also warned commercial vessels against relying on instructions issued by US Central Command (CENTCOM).
It urged ships to follow Iran's maritime regulations and avoid restricted sea routes.
The claims have raised fresh concerns over maritime security near the Strait of Hormuz, one of the world's most important oil shipping routes.