IRNA news agency, citing the unknown source, said the crew had been evacuated and were safe.
The source added that 44 sailors were transferred to Iran's port city of Jask in the southern province of Hormozgan as a result of the rescue operation.
Following the attack, Iran dispatched an advanced Search and Rescue (SAR) vessel, Naji (rescuer) 10, to the Sea of Oman for relief and rescue operations.
Crude oil futures jumped on Thursday following reports of explosions in the Sea of Oman.
Benchmark Brent crude oil rises 4% in trading to over $62 a barrel after the incident, Bloomberg reported.
Reuters identified the tankers as the Marshal Islands-flagged Front Altair and the Panama-flagged Kokuka Courageous.