The Tasnim news agency said that social media reports alleging that a Revolutionary Guard navy commander had been targeted in the explosion were "completely false".
The state news agency IRNA published a photo of the partially destroyed front of a multi-storey residential building.
Iranian media said the blast was under investigation but provided no further information.
Iranian authorities could not immediately be contacted for comment.
Separately, four people were killed after a gas explosion in the city of Ahvaz near the Iraqi border, according to the state-run Tehran Times.
No further information was immediately available.
Two Israeli officials told Reuters that Israel was not involved in Saturday's blasts, which come amid heightened tensions between Iran and the US over Iran's crackdown on protests and over the country's nuclear program.
The Pentagon did not immediately respond to a request for comment.
US President Donald Trump said on January 22 an "armada" was heading toward Iran.
Multiple sources said on Friday that Trump was weighing options against Iran that include targeted strikes on security forces.
Earlier on Saturday, Iranian President Masoud Pezeshkian accused US, Israeli and European leaders of exploiting Iran's economic problems, inciting unrest and providing people with the means to "tear the nation apart".
Bandar Abbas, home to Iran's most important container port, lies on the Strait of Hormuz, a vital waterway between Iran and Oman which handles about a fifth of the world's seaborne oil.
The port suffered a major explosion last April that killed dozens and injured more than 1000 people.
An investigative committee at the time blamed the blast on shortcomings in adherence to principles of civil defence and security.
Iran has been rocked by protests that erupted in December over economic hardship and have posed one of the toughest challenges to the country's clerical rulers.
At least 5000 people were killed in the protests, including 500 members of the security forces, an Iranian official told Reuters.
with DPA
