The agency said a court order, stemming from a private lawsuit, had been given to Iran's Ministry of Telecommunications to ban the site. However, users in the capital, Tehran, still could access the application around noon today.
Some previous reports in Iran of websites and Internet applications being blocked never materialised.
Officials with Instagram Inc declined to comment.
However, Instagram's owner Facebook is already banned in the country, along with other social websites like Twitter and YouTube. That's despite senior government leaders like Foreign Minister Mohammad Javad Zarif being active on Twitter.
While top officials have unfettered access to social media, Iran's youth and technological-savvy citizens use proxy servers or other workarounds to bypass the controls.
Social media has offered a new way for Rouhani and his administration to reach out to the West as it negotiates with world powers over the country's contested nuclear programme.
Rouhani himself has opposed blocking social network sites before authorities create local alternatives.
"We should see the cyberworld as an opportunity," Rouhani said last week, according to the official IRNA news agency. "Why are we so shaky? Why don't we trust our youth?"
Earlier this week, police arrested and showed six young Iranian on state television over them posting online a video showing them dancing to the Pharrell Williams' song "Happy." Last week, hard-liners marched over women not being significantly veiled and dressing provocatively.
Online, that battle continues. Iran's police chief said last year that the Islamic Republic was developing new software to control social networking sites, though it is unclear whether it was ever put to use.
In 2012, Iran created the Supreme Council of Cyberspace, tasked with preventing harm to Iranians who go online. Khamenei, who has the final say on all state matters, ordered the creation of the council in order to fight what he called a "culture invasion" aimed at undermining the Islamic Republic.
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