The blast occurred on Saturday as Iran began a third round of nuclear talks with the United States in Oman, although the cause of the explosion was not immediately clear.
"The source of this incident was the explosion of several containers stored in the Shahid Rajaee Port wharf area," a local crisis management official told state TV.
"We are currently evacuating and transferring the injured to medical centres."
Citing the spokesperson for first responders, state TV reported that at least 281 people had been injured.
It was not yet clear whether there were any fatalities.
The semi-official Tasnim news agency posted footage of injured men lying on the road being tended to amid scenes of confusion.
Efforts were ongoing to extinguish a significant fire, with the port's customs saying that trucks were being evacuated from the area and that the container yard where the explosion occurred likely contained "dangerous goods and chemicals".
State TV said: "negligence in handling flammable materials was a contributing factor" in the explosion.
Oil facilities were not affected by the blast as the National Iranian Petroleum Refining and Distribution Company said.
"The explosion and fire in Shahid Rajaee Port have no connection to refineries, fuel tanks, distribution complexes and oil pipelines related to this company," the statement said.
The large blast shattered windows within a radius of several kilometres, Iranian media said, with footage shared online showing a mushroom cloud forming following the explosion.
Fars news said the blast was heard in Qeshm, an island 26 kilometres south of Bandar Abbas.
In 2020, computers at the same port were hit by a cyberattack that caused massive backups on waterways and roads leading to the facility.
The Washington Post had reported that Iran's arch-foe Israel appeared to be behind that incident as retaliation for an earlier Iranian cyberattack.
There was no immediate comment from Israeli military or Prime Minister Benjamin Netanyahu's office when asked for comment on whether Israel was in any way involved in the explosion.
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