Iran's army also identified the Kharg as a "training ship" and confirmed there were nearly 400 crew and trainees on board, before adding all of them were safely evacuated.
The ship's crew were safely evacuated and no casualties were reported.
The statement did not give the cause of the fire.
The fire broke out in "one of the systems" of the ship, a navy statement said without elaborating.
The statement reported by Tasnim News Agency said the vessel had left for a "training mission" in worldwide waters days ago.
Kharg had been on a "training, intelligence and combat mission" in global waters along with Alborz, an Alvand-class frigate, according to a statement from the naval force of the regular Iranian army May 9.
The Kharg - described by State TV and the semiofficial news agencies as a "training ship" - can lift heavy cargo and serve as a launch point for helicopters. The ship was built in Britain and launched in 1977, before entering the Iranian navy in 1984. In recent months, however, the navy launched a slightly larger commercial tanker called the Makran it converted into serving a similar function as the Kharg.
The ship caught fire at 11 am (0630 GMT) on Tuesday as it was in "domestic waters" during "a training mission", Iran's Tasnim news agency quoted the navy's head of public relations Behzad Jahanian as saying.
The port city of Jask, near which the Kharg went down, lies close to the Strait of Hormuz, the strategic chokepoint at the head of the Gulf through which a fifth of world oil output passes. However, it comes after a series of mysterious explosions that began in 2019 targeting ships in the Gulf of Oman.
In April, an Iranian ship called the MV Saviz believed to be a Guard base and anchored for years in the Red Sea off Yemen was targeted in an attack suspected to have been carried out by Israel.
Iran has refused to recognize Israel since the Islamic revolution in 1979 that toppled the US-backed Shah. In 2018, an Iranian destroyer sank in the Caspian Sea.
Last year, an Iranian naval vessel mistakenly hit another with a missile during a training exercise near Jask, killing 19 sailors and wounding 15 others.