State media said both tankers were carrying about 2 million barrels of crude oil.
There was no independent confirmation of the reports.
IRNA reported that the vessels had switched off their positioning and radar systems and attempted to use an unauthorised route through the strategic waterway.
The second vessel was left immobilised after striking a mine, it added.
State media earlier reported that the other tanker had also struck a mine while attempting to transit the strait via a route not authorised by Iran.
The incidents come amid heightened tensions around the strait, a key oil shipping route.
The Strait of Hormuz, which is only 35 to 40km wide at its narrowest point, has become the central point of conflict between Iran and the United States.
Disruptions to shipping in the waterway due to the US-Israeli war on Iran have boosted global energy prices and inflation.
Maritime officials said on Wednesday that a container ship and a dry bulk carrier sank near the strait after being hit by projectiles in separate incidents.
Attacks around the waterway have surged over the past two weeks, with Iran saying it is stepping up strikes in response to the US blockade of its ports and tougher sanctions imposed last month.
with DPA
