Iran seized control of the strait after a war broke out against the US and Israel in late February, choking off the vital shipping route which normally carries about a fifth of the worldâs oil.
The Islamic republic has demanded that all ships seek its authorisation before transiting.
âAn oil tanker, which was in violation, struck a naval mine south of the Strait of Hormuz, resulting in an explosion and a fire in its engine room,â Iranian state media quoted the Guards as saying.
The tanker was travelling in the straitâs âunauthorised southern routeâ and had disabled its positioning and navigation systems, the statement said.
It came a day after the Guards said two oil tankers caught fire in the strait, both after hitting mines.
The Guardsâ naval commander Admiral Ali Ozmaei warned this week that any vessel that deactivated its navigation systems would be considered âhostileâ.
The US has imposed a naval counter-blockade on Iranian oil exports in response to Tehranâs blockade on the waterway.