Kremlin critic Alexei Navalny, who organised the protest, was detained near the entrance to his home earlier on Monday as he was heading to the protest venue.
There is a risk of violence as Mr Navalny's supporters descend on Moscow city centre for an unauthorised protest.
There have been several arrests at protests in the east of the country.
Mr Navalny said contractors hired to build a stage at the agreed-upon venue could not do their work. Russian opposition leader Alexei Navalny, aiming to repeat the nationwide protests that rattled the Kremlin three months ago, has called for the protest to be moved to Tverskaya street, one of Moscow's main thoroughfares, prompting a massive police presence.
Police have warned that they will take action if protesters break the law.
A regional security official, Vladimir Chernikov, told Ekho Moskvy radio that police would not interfere with demonstrators on the street - as long as they did not carry placards or shout slogans.
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Navalny, who is mounting a long-shot bit to unseat Putin in a presidential election next year, had called for mass protests in Moscow and other cities against what he says is a corrupt system of rule overseen by Russian President Vladimir Putin.
Navalny announced the change less than 24 hours before the planned anticorruption protests across the country on the Russia Day holiday.
On everyone's lips is the huge protest on Monday to demand an inquiry into corruption at the highest echelons of power. He had also demanded that Russia's Prime Minister Dmitry Medvedev tender his resignation. In April, he suffered damage to one eye after an attacker doused his face with a green antiseptic liquid.
Navalny's Fund for Fighting Corruption had been providing updates on protests throughout the country Monday.
To mark Russia Day, the City Hall closed off Tverskaya Street to road traffic and set up a chain of events like reenactment of various eras in Russian history, from World War I trenches to a Rennaissance fair and swordfighting.
The wife of Russian opposition leader Alexei Navalny says that he has been arrested outside his Moscow home on his way to the main demonstration in the capital.