"Twenty-nine people were detained by police for breaches of public order," the city police's press service said.
An AFP journalist at the scene said he witnessed around 30 people being detained as they attempted to carry out a peaceful march.
Among them was a 16-year-old boy called Pavel Dyatlov who became a symbol of youth protest in last week's rally when he was photographed climbing up a lamppost. He was detained in that protest, too.
Navalny, who is currently serving a 15-day sentence behind bars for disobeying police at last Sunday's event, has distanced himself from the latest protest.
More From This Section
"He knows absolutely nothing about this," his spokeswoman Kira Yarmysh wrote on Twitter.
Navalny last Sunday organised protests in cities across Russia, most of which were not authorised by municipal officials. The largest in Moscow saw about 500 people detained according to police, while OVD-Info put the total at almost 1,000.
Posts on Facebook linked the latest protest to a little-known nationalist group.
Police in helmets and body armour swiftly moved to arrest demonstrators.
The authorities earlier had laid on a massive police presence in anticipation of an unauthorised protest at 0900 GMT after calls were posted online to rally on Red Square.
Journalists saw only a handful of activists, however, some of whom voiced support for President Vladimir Putin. OVD-Info reported that a total of 11 were detained.
In the large Siberian city of Novosibirsk, several hundred people turned out for an opposition rally that was permitted by the authorities, Interfax news agency reported, saying around 400 people took part.