It said a "limited gathering" began before noon when some shop owners at the Aladdin and Charsou malls, two of the city's main mobile and tech markets, marched down Jomhouri Street to "protest problems caused by power cuts".
"At the same time, a group tried to use the dissatisfaction and make it political" by chanting "norm-breaking slogans", the website added.
The term "norm-breaking" is regularly used by Iranian media to refer to slogans critical of the authorities in the Islamic republic.
A video posted on Twitter by the ultraconservative Fars news agency showed protesters blocking the busy street, with security forces on motorcycles present nearby.
Fars said the gathering comprised "about 50 people", some of whom chanted "political slogans".
These included "Neither Gaza nor Lebanon, my life for Iran" and "Police, support us", the video footage showed.
Iran does not recognise Israel, and support for the Palestinian cause and groups such as Lebanon's Hezbollah has been a pillar of its foreign policy since soon after the 1979 Islamic revolution.
A spokesman for Iran's power company told Fars that Aladdin mall had been notified ahead of a two-hour power cut over "excessive usage".
At about 4 pm (1130 GMT) on Monday, there was a police presence around Aladdin, but traffic volumes appeared normal and power there had been restored, an AFP journalist said.
Rolling blackouts began in Tehran and other large cities this month, with officials blaming them on the impact of drought on hydroelectric power generation, as well as surging demand.
Cuts in the capital have reduced in frequency since the first week of July when unannounced blackouts lasted for hours, but the energy ministry still notifies people ahead of planned cuts because of an overburdened grid.
There have also been protests because over water.
The southwestern province of Khuzestan has been gripped by drought since March, with protests about water shortages erupting in several towns and cities since July 15.
Iranian media and officials have reported at least three people killed in the province, including a police officer and a protester, with "opportunists" and "rioters" accused of shooting at demonstrators and security forces.
State television reported a fourth person killed on Thursday in the western province of Lorestan where people had taken to the streets "on the pretext of water problems in Khuzestan".
